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Aufgaben:Aufgabe 2.7Z: Huffman-Codierung für Zweiertupel einer Ternärquelle - Versionsgeschichte
2024-03-29T14:18:38Z
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Guenter am 11. August 2021 um 09:49 Uhr
2021-08-11T09:49:31Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 11. August 2021, 09:49 Uhr</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''Hinweise:'' </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''Hinweise:'' </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Die Aufgabe gehört zum Kapitel&nbsp; [[Informationstheorie/Entropiecodierung_nach_Huffman|Entropiecodierung nach Huffman]].</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Die Aufgabe gehört zum Kapitel&nbsp; [[Informationstheorie/Entropiecodierung_nach_Huffman|Entropiecodierung nach Huffman]].</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird auf die Seite&nbsp; [[Informationstheorie/Entropiecodierung_nach_Huffman#Anwendung_der_Huffman.E2.80.93Codierung_auf_.7F.27.22.60UNIQ-<del class="diffchange diffchange-inline">MathJax164</del>-QINU.60.22.27.7F.E2.80.93Tupel|Anwendung der Huffman-Codierung auf&nbsp; $k$-Tupel]]&nbsp; Bezug genommen.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird auf die Seite&nbsp; [[Informationstheorie/Entropiecodierung_nach_Huffman#Anwendung_der_Huffman.E2.80.93Codierung_auf_.7F.27.22.60UNIQ-<ins class="diffchange diffchange-inline">MathJax169</ins>-QINU.60.22.27.7F.E2.80.93Tupel|Anwendung der Huffman-Codierung auf&nbsp; $k$-Tupel]]&nbsp; Bezug genommen.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Eine vergleichbare Aufgabenstellung mit binären Eingangssymbolen wird in der&nbsp; [[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe 2.7]]&nbsp; behandelt.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Eine vergleichbare Aufgabenstellung mit binären Eingangssymbolen wird in der&nbsp; [[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe 2.7]]&nbsp; behandelt.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Bezeichnen Sie die möglichen Zweiertupel mit &nbsp; &nbsp; $\rm XX = A$,&nbsp; &nbsp;$\rm XY = B$,&nbsp; &nbsp;$\rm XZ = C$,&nbsp;&nbsp; $\rm YX = D$,&nbsp; &nbsp;$\rm YY = E$,&nbsp; &nbsp;$\rm YZ = F$,&nbsp; &nbsp;$\rm ZX = G$,&nbsp; &nbsp;$\rm ZY = H$,&nbsp; &nbsp;$\rm ZZ = I$.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Bezeichnen Sie die möglichen Zweiertupel mit &nbsp; &nbsp; $\rm XX = A$,&nbsp; &nbsp;$\rm XY = B$,&nbsp; &nbsp;$\rm XZ = C$,&nbsp;&nbsp; $\rm YX = D$,&nbsp; &nbsp;$\rm YY = E$,&nbsp; &nbsp;$\rm YZ = F$,&nbsp; &nbsp;$\rm ZX = G$,&nbsp; &nbsp;$\rm ZY = H$,&nbsp; &nbsp;$\rm ZZ = I$.</div></td></tr>
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Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.7Z:_Huffman-Codierung_f%C3%BCr_Zweiertupel_einer_Tern%C3%A4rquelle&diff=29364&oldid=prev
Guenter am 25. Januar 2020 um 16:26 Uhr
2020-01-25T16:26:59Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 25. Januar 2020, 16:26 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16" >Zeile 16:</td>
<td colspan="2" class="diff-lineno">Zeile 16:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Die Grafik zeigt den Huffman&ndash;Baum, wenn man den Huffman&ndash;Algorithmus auf Einzelsymbole anwendet, also den Fall&nbsp; $k= 1$. <br>In der Teilaufgabe '''(2)''' sollen Sie den entsprechenden Huffman&ndash;Code angeben, wenn vorher Zweiertupel gebildet werden&nbsp; $(k=2)$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Die Grafik zeigt den Huffman&ndash;Baum, wenn man den Huffman&ndash;Algorithmus auf Einzelsymbole anwendet, also den Fall&nbsp; $k= 1$. <br>In der Teilaufgabe<ins class="diffchange diffchange-inline">&nbsp; </ins>'''(2)'''<ins class="diffchange diffchange-inline">&nbsp; </ins>sollen Sie den entsprechenden Huffman&ndash;Code angeben, wenn vorher Zweiertupel gebildet werden&nbsp; $(k=2)$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l67" >Zeile 67:</td>
<td colspan="2" class="diff-lineno">Zeile 67:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(1)'''&nbsp; Die mittlere Codewortlänge ergibt sich mit &nbsp;$p_{\rm X} = 0.7$, &nbsp;$L_{\rm X} = 1$, &nbsp;$p_{\rm Y} = 0.2$, &nbsp;$L_{\rm Y} = 2$, &nbsp;$p_{\rm Z} = 0.1$, &nbsp;$L_{\rm Z} = 2$ zu</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(1)'''&nbsp; Die mittlere Codewortlänge ergibt sich mit &nbsp;$p_{\rm X} = 0.7$, &nbsp;$L_{\rm X} = 1$, &nbsp;$p_{\rm Y} = 0.2$, &nbsp;$L_{\rm Y} = 2$, &nbsp;$p_{\rm Z} = 0.1$, &nbsp;$L_{\rm Z} = 2$ zu</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$L_{\rm M} = p_{\rm X} \cdot 1 + (p_{\rm Y} + p_{\rm Z}) \cdot 2 \hspace{0.15cm}\underline{= 1.3\,\,{\rm bit/Quellensymbol}}\hspace{0.05cm}. $$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$L_{\rm M} = p_{\rm X} \cdot 1 + (p_{\rm Y} + p_{\rm Z}) \cdot 2 \hspace{0.15cm}\underline{= 1.3\,\,{\rm bit/Quellensymbol}}\hspace{0.05cm}. $$</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Dieser Wert liegt noch deutlich über der Quellenentropie $H = 1.157$ bit/Quellensymbol.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>Dieser Wert liegt noch deutlich über der Quellenentropie<ins class="diffchange diffchange-inline">&nbsp; </ins>$H = 1.157$<ins class="diffchange diffchange-inline">&nbsp; </ins>bit/Quellensymbol.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''(2)'''&nbsp; Es gibt $M' = M^k = 3^2<del class="diffchange diffchange-inline">$ </del>= 9 Zweiertupel mit folgenden Wahrscheinlichkeiten:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''(2)'''&nbsp; Es gibt<ins class="diffchange diffchange-inline">&nbsp; </ins>$M<ins class="diffchange diffchange-inline">\hspace{0.03cm}</ins>' = M^k = 3^2 = 9<ins class="diffchange diffchange-inline">$&nbsp; </ins>Zweiertupel mit folgenden Wahrscheinlichkeiten:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:P_ID2459__Inf_Z_2_7c.png|right|frame|Huffman–Baum für Ternärquelle und Zweiertupel]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:P_ID2459__Inf_Z_2_7c.png|right|frame|Huffman–Baum für Ternärquelle und Zweiertupel]]</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l82" >Zeile 82:</td>
<td colspan="2" class="diff-lineno">Zeile 83:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$p_{\rm H} = \rm Pr(ZY) = 0.1 \cdot 0.2 = 0.02,$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$p_{\rm H} = \rm Pr(ZY) = 0.1 \cdot 0.2 = 0.02,$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$p_{\rm I} = \rm Pr(ZZ) = 0.1 \cdot 0.1 = 0.01.$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$p_{\rm I} = \rm Pr(ZZ) = 0.1 \cdot 0.1 = 0.01.$$</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><br clear=all></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''(3)'''&nbsp; Die Grafik zeigt den Huffman&ndash;Baum für die Anwendung mit $k = 2$.<ins class="diffchange diffchange-inline">&nbsp; </ins>Damit erhält man</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''(3)'''&nbsp; Die Grafik zeigt den Huffman&ndash;Baum für die Anwendung mit $k = 2$.</div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Damit erhält man</div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* für die einzelnen Zweiertupels folgende Binärcodierungen: <br></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* für die einzelnen Zweiertupels folgende Binärcodierungen: <br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: &nbsp; &nbsp; $\rm XX = A$ &nbsp; &#8594; &nbsp; '''0''', &nbsp; &nbsp; $\rm XY = B$ &nbsp; &#8594; &nbsp; '''111''', &nbsp; &nbsp; $\rm XZ = C$ &nbsp; &#8594; &nbsp; <b>1011</b>, </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: &nbsp; &nbsp; $\rm XX = A$ &nbsp; &#8594; &nbsp; '''0''', &nbsp; &nbsp; $\rm XY = B$ &nbsp; &#8594; &nbsp; '''111''', &nbsp; &nbsp; $\rm XZ = C$ &nbsp; &#8594; &nbsp; <b>1011</b>, </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: &nbsp; &nbsp; $\rm YX = D$ &nbsp; &#8594; &nbsp; <b>110</b>, &nbsp; &nbsp; $\rm YY = E$ &nbsp; &#8594; &nbsp; <b>1000</b>, &nbsp; &nbsp; $\rm YZ = F$ &nbsp; &#8594; &nbsp; <b>10010</b>,</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: &nbsp; &nbsp; $\rm YX = D$ &nbsp; &#8594; &nbsp; <b>110</b>, &nbsp; &nbsp; $\rm YY = E$ &nbsp; &#8594; &nbsp; <b>1000</b>, &nbsp; &nbsp; $\rm YZ = F$ &nbsp; &#8594; &nbsp; <b>10010</b>,</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: &nbsp; &nbsp; $\rm ZX = G$ &nbsp; &#8594; &nbsp; <b>1010</b>, &nbsp; &nbsp; $\rm ZY = H$ &nbsp; &#8594; &nbsp; <b>100111</b>, &nbsp; &nbsp; $\rm ZZ =I$ &nbsp; &#8594; &nbsp; <b>100110</b><del class="diffchange diffchange-inline">. </del> </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>: &nbsp; &nbsp; $\rm ZX = G$ &nbsp; &#8594; &nbsp; <b>1010</b>, &nbsp; &nbsp; $\rm ZY = H$ &nbsp; &#8594; &nbsp; <b>100111</b>, &nbsp; &nbsp; $\rm ZZ =I$ &nbsp; &#8594; &nbsp; <b>100110</b><ins class="diffchange diffchange-inline">; </ins> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* für die mittlere Codewortlänge:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* für die mittlere Codewortlänge:</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l97" >Zeile 97:</td>
<td colspan="2" class="diff-lineno">Zeile 96:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''(4)'''&nbsp; Richtig ist die <u>Aussage 1</u>, auch wenn $L_{\rm M}$ mit wachsendem $k$ nur sehr langsam abfällt.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''(4)'''&nbsp; Richtig ist die <u>Aussage 1</u>, auch wenn<ins class="diffchange diffchange-inline">&nbsp; </ins>$L_{\rm M}$<ins class="diffchange diffchange-inline">&nbsp; </ins>mit wachsendem<ins class="diffchange diffchange-inline">&nbsp; </ins>$k$<ins class="diffchange diffchange-inline">&nbsp; </ins>nur sehr langsam abfällt.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Die letzte Aussage ist falsch, da $L_{\rm M}$ auch für $k &#8594; &#8734;$ nicht kleiner sein kann als $H = 1.157$ bit/Quellensymbol.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Die letzte Aussage ist falsch, da<ins class="diffchange diffchange-inline">&nbsp; </ins>$L_{\rm M}$<ins class="diffchange diffchange-inline">&nbsp; </ins>auch für<ins class="diffchange diffchange-inline">&nbsp; </ins>$k &#8594; &#8734;$<ins class="diffchange diffchange-inline">&nbsp; </ins>nicht kleiner sein kann als<ins class="diffchange diffchange-inline">&nbsp; </ins>$H = 1.157$<ins class="diffchange diffchange-inline">&nbsp; </ins>bit/Quellensymbol.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Aber auch die zweite Aussage ist nicht unbedingt richtig: &nbsp; Da mit $k = 2$ weiterhin $L_{\rm M} > H$ gilt, kann $k = 3$ zu einer weiteren Verbesserung führen.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Aber auch die zweite Aussage ist nicht unbedingt richtig: &nbsp; Da mit<ins class="diffchange diffchange-inline">&nbsp; </ins>$k = 2$<ins class="diffchange diffchange-inline">&nbsp; </ins>weiterhin<ins class="diffchange diffchange-inline">&nbsp; </ins>$L_{\rm M} > H$<ins class="diffchange diffchange-inline">&nbsp; </ins>gilt, kann<ins class="diffchange diffchange-inline">&nbsp; </ins>$k = 3$<ins class="diffchange diffchange-inline">&nbsp; </ins>zu einer weiteren Verbesserung führen.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{ML-Fuß}}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{ML-Fuß}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>
Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.7Z:_Huffman-Codierung_f%C3%BCr_Zweiertupel_einer_Tern%C3%A4rquelle&diff=29363&oldid=prev
Guenter am 25. Januar 2020 um 16:18 Uhr
2020-01-25T16:18:52Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 25. Januar 2020, 16:18 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l36" >Zeile 36:</td>
<td colspan="2" class="diff-lineno">Zeile 36:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><quiz display=simple></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><quiz display=simple></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Wie groß ist die mittlere Codewortlänge, wenn der Huffman&ndash;Algorithmus direkt auf die ternären Quellensymbole&nbsp; $\rm X$,nbsp; $\rm Y$nbsp; <del class="diffchange diffchange-inline">undnbsp</del>; $\rm Z$nbsp; angewendet wird? </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Wie groß ist die mittlere Codewortlänge, wenn der Huffman&ndash;Algorithmus direkt auf die ternären Quellensymbole&nbsp; $\rm X$,<ins class="diffchange diffchange-inline">&</ins>nbsp; $\rm Y$<ins class="diffchange diffchange-inline">&</ins>nbsp; <ins class="diffchange diffchange-inline">und&nbsp</ins>; $\rm Z$<ins class="diffchange diffchange-inline">&</ins>nbsp; angewendet wird? </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$\underline{k=1}\text{:} \hspace{0.25cm}L_{\rm M} \ = \ $ { 1.3 3% } $\ \rm bit/Quellensymbol$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$\underline{k=1}\text{:} \hspace{0.25cm}L_{\rm M} \ = \ $ { 1.3 3% } $\ \rm bit/Quellensymbol$</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l53" >Zeile 53:</td>
<td colspan="2" class="diff-lineno">Zeile 53:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Welche der folgenden Aussagen sind zutreffend, wenn man mehr als zwei Ternärzeichen <del class="diffchange diffchange-inline">zusammenfasstnbsp</del>; $(k>2)$?</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Welche der folgenden Aussagen sind zutreffend, wenn man mehr als zwei Ternärzeichen <ins class="diffchange diffchange-inline">zusammenfasst&nbsp</ins>; $(k>2)$?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="[]"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="[]"}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>+ $L_{\rm M}$&nbsp; fällt monoton mit steigendem &nbsp;$k$&nbsp; ab.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>+ $L_{\rm M}$&nbsp; fällt monoton mit steigendem &nbsp;$k$&nbsp; ab.</div></td></tr>
</table>
Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.7Z:_Huffman-Codierung_f%C3%BCr_Zweiertupel_einer_Tern%C3%A4rquelle&diff=29362&oldid=prev
Guenter am 25. Januar 2020 um 16:16 Uhr
2020-01-25T16:16:49Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 25. Januar 2020, 16:16 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3" >Zeile 3:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:P_ID2458__Inf_Z_2_7.png|right|frame|Huffman–Baum für Ternärquelle]]</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:P_ID2458__Inf_Z_2_7.png|right|frame|Huffman–Baum für <ins class="diffchange diffchange-inline"><br>eine </ins>Ternärquelle]]</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Wir betrachten den gleichen Sachverhalt wie in der [[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe A2.7]]: &nbsp; Der Huffman&ndash;Algorithmus führt zu einem besseren Ergebnis, das heißt zu einer kleineren mittleren Codewortlänge $L_{\rm M}$, wenn man ihn nicht auf einzelne Symbole anwendet, sondern vorher $k$&ndash;Tupel bildet. Dadurch erhöht man den Symbolumfang von $M$ auf $M' = M^k$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Wir betrachten den gleichen Sachverhalt wie in der<ins class="diffchange diffchange-inline">&nbsp; </ins>[[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe A2.7]]: &nbsp; </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>Der Huffman&ndash;Algorithmus führt zu einem besseren Ergebnis, das heißt zu einer kleineren mittleren Codewortlänge<ins class="diffchange diffchange-inline">&nbsp; </ins>$L_{\rm M}$, wenn man ihn nicht auf einzelne Symbole anwendet, sondern vorher<ins class="diffchange diffchange-inline">&nbsp; </ins>$k$&ndash;Tupel bildet.<ins class="diffchange diffchange-inline">&nbsp; </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>Dadurch erhöht man den Symbolumfang von<ins class="diffchange diffchange-inline">&nbsp; </ins>$M$<ins class="diffchange diffchange-inline">&nbsp; </ins>auf $M<ins class="diffchange diffchange-inline">\hspace{0.03cm}</ins>' = M^k$.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Für die hier betrachtete Nachrichtenquelle gilt:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Für die hier betrachtete Nachrichtenquelle gilt:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Symbolumfang: &nbsp; $M = 3$,</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Symbolumfang: &nbsp; $M = 3$,</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Symbolvorrat: &nbsp; $\{$ $\rm X$, $\rm Y$, $\rm Z$ $\}$,</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Symbolvorrat: &nbsp; $\{$ $\rm X$,<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm Y$,<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm Z$ $\}$,</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Wahrscheinlichkeiten: &nbsp; $p_{\rm X} = 0.7$, $p_{\rm Y} = 0.2$, $p_{\rm Z} = 0.1$,</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Wahrscheinlichkeiten: &nbsp; $p_{\rm X} = 0.7$,<ins class="diffchange diffchange-inline">&nbsp; </ins>$p_{\rm Y} = 0.2$,<ins class="diffchange diffchange-inline">&nbsp; </ins>$p_{\rm Z} = 0.1$,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Entropie: &nbsp; $H = 1.157 \ \rm bit/Ternärsymbol$.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Entropie: &nbsp; $H = 1.157 \ \rm bit/Ternärsymbol$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Die Grafik zeigt den Huffman&ndash;Baum, wenn man den Huffman&ndash;Algorithmus auf Einzelsymbole anwendet, also den Fall $k= 1$. In der Teilaufgabe '''(2)''' sollen Sie den entsprechenden Huffman&ndash;Code angeben, wenn vorher Zweiertupel gebildet werden $(k=2)$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Die Grafik zeigt den Huffman&ndash;Baum, wenn man den Huffman&ndash;Algorithmus auf Einzelsymbole anwendet, also den Fall<ins class="diffchange diffchange-inline">&nbsp; </ins>$k= 1$. <ins class="diffchange diffchange-inline"><br></ins>In der Teilaufgabe '''(2)''' sollen Sie den entsprechenden Huffman&ndash;Code angeben, wenn vorher Zweiertupel gebildet werden<ins class="diffchange diffchange-inline">&nbsp; </ins>$(k=2)$.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l20" >Zeile 20:</td>
<td colspan="2" class="diff-lineno">Zeile 26:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''Hinweise:'' </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''Hinweise:'' </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Die Aufgabe gehört zum Kapitel [[Informationstheorie/Entropiecodierung_nach_Huffman|Entropiecodierung nach Huffman]].</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Die Aufgabe gehört zum Kapitel<ins class="diffchange diffchange-inline">&nbsp; </ins>[[Informationstheorie/Entropiecodierung_nach_Huffman|Entropiecodierung nach Huffman]].</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird auf die Seite [[Informationstheorie/Entropiecodierung_nach_Huffman#Anwendung_der_Huffman.E2.80.93Codierung_auf_.7F.27.22.60UNIQ-<del class="diffchange diffchange-inline">MathJax153</del>-QINU.60.22.27.7F.E2.80.93Tupel|Anwendung der Huffman-Codierung auf k-Tupel]] Bezug genommen.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird auf die Seite<ins class="diffchange diffchange-inline">&nbsp; </ins>[[Informationstheorie/Entropiecodierung_nach_Huffman#Anwendung_der_Huffman.E2.80.93Codierung_auf_.7F.27.22.60UNIQ-<ins class="diffchange diffchange-inline">MathJax164</ins>-QINU.60.22.27.7F.E2.80.93Tupel|Anwendung der Huffman-Codierung auf<ins class="diffchange diffchange-inline">&nbsp; $</ins>k<ins class="diffchange diffchange-inline">$</ins>-Tupel]]<ins class="diffchange diffchange-inline">&nbsp; </ins>Bezug genommen.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Eine vergleichbare Aufgabenstellung mit binären Eingangssymbolen wird in der [[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe 2.7]] behandelt.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Eine vergleichbare Aufgabenstellung mit binären Eingangssymbolen wird in der<ins class="diffchange diffchange-inline">&nbsp; </ins> [[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe 2.7]]<ins class="diffchange diffchange-inline">&nbsp; </ins>behandelt.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Bezeichnen Sie die möglichen Zweiertupel mit &nbsp; &nbsp; $\rm XX = A$,&nbsp;&nbsp;$\rm XY = B$,&nbsp;&nbsp;$\rm XZ = C$,&nbsp;&nbsp; $\rm YX = D$,&nbsp;&nbsp;$\rm YY = E$,&nbsp;&nbsp;$\rm YZ = F$,&nbsp;&nbsp;$\rm ZX = G$,&nbsp;&nbsp;$\rm ZY = H$,&nbsp;&nbsp;$\rm ZZ = I$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Bezeichnen Sie die möglichen Zweiertupel mit &nbsp; &nbsp; $\rm XX = A$,&nbsp; &nbsp;$\rm XY = B$,&nbsp; &nbsp;$\rm XZ = C$,&nbsp;&nbsp; $\rm YX = D$,&nbsp; &nbsp;$\rm YY = E$,&nbsp; &nbsp;$\rm YZ = F$,&nbsp; &nbsp;$\rm ZX = G$,&nbsp; &nbsp;$\rm ZY = H$,&nbsp; &nbsp;$\rm ZZ = I$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l30" >Zeile 30:</td>
<td colspan="2" class="diff-lineno">Zeile 36:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><quiz display=simple></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><quiz display=simple></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Wie groß ist die mittlere Codewortlänge, wenn der Huffman&ndash;Algorithmus direkt auf die ternären Quellensymbole $\rm X$, $\rm Y$ <del class="diffchange diffchange-inline">und </del>$\rm Z$ angewendet wird? </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Wie groß ist die mittlere Codewortlänge, wenn der Huffman&ndash;Algorithmus direkt auf die ternären Quellensymbole<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm X$,<ins class="diffchange diffchange-inline">nbsp; </ins>$\rm Y$<ins class="diffchange diffchange-inline">nbsp; undnbsp; </ins>$\rm Z$<ins class="diffchange diffchange-inline">nbsp; </ins>angewendet wird? </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$\underline{k=1}\text{:} \hspace{0.25cm}L_{\rm M} \ = \ $ { 1.3 3% } $\ \rm bit/Quellensymbol$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$\underline{k=1}\text{:} \hspace{0.25cm}L_{\rm M} \ = \ $ { 1.3 3% } $\ \rm bit/Quellensymbol$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Wie groß sind <del class="diffchange diffchange-inline"> </del>die Tupel&ndash;Wahrscheinlichkeiten? Insbesondere:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Wie groß sind <ins class="diffchange diffchange-inline">hier </ins>die Tupel&ndash;Wahrscheinlichkeiten? Insbesondere:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm A} = \rm Pr(XX)\ = \ $ { 0.49 3% }</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm A} = \rm Pr(XX)\ = \ $ { 0.49 3% }</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l47" >Zeile 47:</td>
<td colspan="2" class="diff-lineno">Zeile 53:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Welche der folgenden Aussagen sind zutreffend, wenn man mehr als zwei Ternärzeichen <del class="diffchange diffchange-inline">zusammenfasst </del>(<del class="diffchange diffchange-inline">$</del>k>2$<del class="diffchange diffchange-inline">)</del>?</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Welche der folgenden Aussagen sind zutreffend, wenn man mehr als zwei Ternärzeichen <ins class="diffchange diffchange-inline">zusammenfasstnbsp; $</ins>(k>2<ins class="diffchange diffchange-inline">)</ins>$?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="[]"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="[]"}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>+ $L_{\rm M}$&nbsp; fällt monoton mit steigendem &nbsp;$k$&nbsp; ab.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>+ $L_{\rm M}$&nbsp; fällt monoton mit steigendem &nbsp;$k$&nbsp; ab.</div></td></tr>
</table>
Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.7Z:_Huffman-Codierung_f%C3%BCr_Zweiertupel_einer_Tern%C3%A4rquelle&diff=26360&oldid=prev
Guenter am 28. September 2018 um 13:08 Uhr
2018-09-28T13:08:36Z
<p></p>
<table class="diff diff-contentalign-left" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 28. September 2018, 13:08 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61" >Zeile 61:</td>
<td colspan="2" class="diff-lineno">Zeile 61:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(1)'''&nbsp; Die mittlere Codewortlänge ergibt sich mit &nbsp;$p_{\rm X} = 0.7$, &nbsp;$L_{\rm X} = 1$, &nbsp;$p_{\rm Y} = 0.2$, &nbsp;$L_{\rm Y} = 2$, &nbsp;$p_{\rm Z} = 0.1$, &nbsp;$L_{\rm Z} = 2$ zu</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(1)'''&nbsp; Die mittlere Codewortlänge ergibt sich mit &nbsp;$p_{\rm X} = 0.7$, &nbsp;$L_{\rm X} = 1$, &nbsp;$p_{\rm Y} = 0.2$, &nbsp;$L_{\rm Y} = 2$, &nbsp;$p_{\rm Z} = 0.1$, &nbsp;$L_{\rm Z} = 2$ zu</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$L_{\rm M} = p_{\rm X} \cdot 1 + (p_{\rm Y} + p_{\rm Z}) \cdot 2 \hspace{0.15cm}\underline{= 1.3\,\,{\rm bit/Quellensymbol}}\hspace{0.05cm}. $$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$L_{\rm M} = p_{\rm X} \cdot 1 + (p_{\rm Y} + p_{\rm Z}) \cdot 2 \hspace{0.15cm}\underline{= 1.3\,\,{\rm bit/Quellensymbol}}\hspace{0.05cm}. $$</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Dieser Wert liegt noch deutlich über der Quellenentropie <del class="diffchange diffchange-inline"><i></del>H<del class="diffchange diffchange-inline"></i> </del>= 1.157 bit/Quellensymbol.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Dieser Wert liegt noch deutlich über der Quellenentropie <ins class="diffchange diffchange-inline">$</ins>H = 1.157<ins class="diffchange diffchange-inline">$ </ins>bit/Quellensymbol.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''(2)'''&nbsp; Es gibt <del class="diffchange diffchange-inline"><i></del>M<del class="diffchange diffchange-inline"></i><sup>&nbsp;</sup>&prime; </del>= <del class="diffchange diffchange-inline"><i></del>M<del class="diffchange diffchange-inline"></i><sup>&nbsp;2</sup> </del>= 3<del class="diffchange diffchange-inline"><sup></del>2<del class="diffchange diffchange-inline"></sup> </del>= 9 Zweiertupel mit folgenden Wahrscheinlichkeiten:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''(2)'''&nbsp; Es gibt <ins class="diffchange diffchange-inline">$</ins>M<ins class="diffchange diffchange-inline">' </ins>= M<ins class="diffchange diffchange-inline">^k </ins>= 3<ins class="diffchange diffchange-inline">^</ins>2<ins class="diffchange diffchange-inline">$ </ins>= 9 Zweiertupel mit folgenden Wahrscheinlichkeiten:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: <del class="diffchange diffchange-inline">&nbsp; &nbsp; <i>p</i><sub></del>A<del class="diffchange diffchange-inline"></sub> </del>= Pr(<del class="diffchange diffchange-inline"><b></del>XX<del class="diffchange diffchange-inline"></b></del>) <del class="diffchange diffchange-inline"><u></del>= 0.49<del class="diffchange diffchange-inline"></u></del>,<del class="diffchange diffchange-inline">&nbsp;&nbsp;&nbsp;<i>p</i><sub></del>B<del class="diffchange diffchange-inline"></sub> </del>= Pr(<del class="diffchange diffchange-inline"><b></del>XY<del class="diffchange diffchange-inline"></b></del>) <del class="diffchange diffchange-inline"><u></del>= 0.14<del class="diffchange diffchange-inline"></u></del>,<del class="diffchange diffchange-inline">&nbsp;&nbsp;&nbsp; <i>p</i><sub></del>C<del class="diffchange diffchange-inline"></sub> </del>= Pr(<del class="diffchange diffchange-inline"><b></del>XZ<del class="diffchange diffchange-inline"></b></del>) <del class="diffchange diffchange-inline"><u></del>= 0.07<del class="diffchange diffchange-inline"></u></del>,</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">[[Datei</ins>:<ins class="diffchange diffchange-inline">P_ID2459__Inf_Z_2_7c.png|right|frame|Huffman–Baum für Ternärquelle und Zweiertupel]]</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: <del class="diffchange diffchange-inline">&nbsp; &nbsp; <i>p</i><sub></del>D<del class="diffchange diffchange-inline"></sub> </del>= Pr(<del class="diffchange diffchange-inline"><b></del>YX<del class="diffchange diffchange-inline"></b></del>) = 0.14,<del class="diffchange diffchange-inline">&nbsp;&nbsp;&nbsp; <i>p</i><sub></del>E<del class="diffchange diffchange-inline"></sub> </del>= Pr(<del class="diffchange diffchange-inline"><b></del>YY<del class="diffchange diffchange-inline"></b></del>) = 0.04,<del class="diffchange diffchange-inline">&nbsp;&nbsp;&nbsp; <i>p</i><sub></del>F<del class="diffchange diffchange-inline"></sub> </del>= Pr(<del class="diffchange diffchange-inline"><b></del>YZ<del class="diffchange diffchange-inline"></b></del>) = 0.02,</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:$$p_{\rm </ins>A<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline">\rm </ins>Pr(XX) <ins class="diffchange diffchange-inline">= 0.7 \cdot 0.7\hspace{0.15cm}\underline{</ins>= 0.49<ins class="diffchange diffchange-inline">}</ins>,<ins class="diffchange diffchange-inline">$$</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: <del class="diffchange diffchange-inline">&nbsp; &nbsp; <i>p</i><sub></del>G<del class="diffchange diffchange-inline"></sub> </del>= Pr(<del class="diffchange diffchange-inline"><b>YX</b></del>) = 0.07,<del class="diffchange diffchange-inline">&nbsp;&nbsp;&nbsp; <i>p</i><sub></del>H<del class="diffchange diffchange-inline"></sub> </del>= Pr(<del class="diffchange diffchange-inline"><b>YY</b></del>) = 0.02,<del class="diffchange diffchange-inline">&nbsp;&nbsp;&nbsp; <i>p</i><sub></del>I<del class="diffchange diffchange-inline"></sub> </del>= Pr(<del class="diffchange diffchange-inline"><b>YZ</b></del>) = 0.01.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:$$p_{\rm </ins>B<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline">\rm </ins>Pr(XY) <ins class="diffchange diffchange-inline">= 0.7 \cdot 0.2\hspace{0.15cm}\underline{</ins>= 0.14<ins class="diffchange diffchange-inline">}</ins>,<ins class="diffchange diffchange-inline">$$</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:$$p_{\rm </ins>C<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline">\rm </ins>Pr(XZ) = 0.7 <ins class="diffchange diffchange-inline">\cdot 0.1\hspace{0.15cm}\underline{= 0.07}</ins>,<ins class="diffchange diffchange-inline">$$</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<ins class="diffchange diffchange-inline">$$p_{\rm </ins>D<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline">\rm </ins>Pr(YX) <ins class="diffchange diffchange-inline">= 0.2 \cdot 0.7 </ins>= 0.14,<ins class="diffchange diffchange-inline">$$</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:$$p_{\rm </ins>E<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline">\rm </ins>Pr(YY) <ins class="diffchange diffchange-inline">= 0.2 \cdot 0.2 </ins>= 0.04,<ins class="diffchange diffchange-inline">$$</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:$$p_{\rm </ins>F<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline">\rm </ins>Pr(YZ) <ins class="diffchange diffchange-inline">= 0.2 \cdot 0.1 </ins>= 0.02,<ins class="diffchange diffchange-inline">$$</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<ins class="diffchange diffchange-inline">$$p_{\rm </ins>G<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline">\rm </ins>Pr(<ins class="diffchange diffchange-inline">ZX</ins>) <ins class="diffchange diffchange-inline">= 0.1 \cdot 0.7 </ins>= 0.07,<ins class="diffchange diffchange-inline">$$</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:$$p_{\rm </ins>H<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline">\rm </ins>Pr(<ins class="diffchange diffchange-inline">ZY</ins>) <ins class="diffchange diffchange-inline">= 0.1 \cdot 0.2 </ins>= 0.02,<ins class="diffchange diffchange-inline">$$</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:$$p_{\rm </ins>I<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline">\rm </ins>Pr(<ins class="diffchange diffchange-inline">ZZ</ins>) <ins class="diffchange diffchange-inline">= 0.1 \cdot 0.1 </ins>= 0.01.<ins class="diffchange diffchange-inline">$$</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''(3)'''&nbsp; Die Grafik zeigt den Huffman&ndash;Baum für die Anwendung mit <del class="diffchange diffchange-inline"><i></del>k<del class="diffchange diffchange-inline"></i> </del>= 2.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''(3)'''&nbsp; Die Grafik zeigt den Huffman&ndash;Baum für die Anwendung mit <ins class="diffchange diffchange-inline">$</ins>k = 2<ins class="diffchange diffchange-inline">$</ins>.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">[[Datei:P_ID2459__Inf_Z_2_7c.png|Huffman–Baum für Ternärquelle und Zweiertupel]]</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Damit erhält man</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Damit erhält man</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* für die einzelnen Zweiertupels folgende Binärcodierungen: <br></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* für die einzelnen Zweiertupels folgende Binärcodierungen: <br></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: <del class="diffchange diffchange-inline"> </del>&nbsp; &nbsp; <del class="diffchange diffchange-inline"><b></del>XX<del class="diffchange diffchange-inline"></b> </del>= <del class="diffchange diffchange-inline"><b></del>A<del class="diffchange diffchange-inline"></b> </del>&#8594; <del class="diffchange diffchange-inline"><b>0</b>,</del>&nbsp;&nbsp;&nbsp;<del class="diffchange diffchange-inline"><b></del>XY<del class="diffchange diffchange-inline"></b> </del>= <del class="diffchange diffchange-inline"><b></del>B<del class="diffchange diffchange-inline"></b> </del>&#8594; <del class="diffchange diffchange-inline"><b>111</b>,</del>&nbsp;&nbsp;&nbsp;<del class="diffchange diffchange-inline"><b></del>XZ<del class="diffchange diffchange-inline"></b> </del>= <del class="diffchange diffchange-inline"><b></del>C<del class="diffchange diffchange-inline"></b> </del>&#8594; <b>1011</b>,&nbsp;&nbsp;&nbsp; <del class="diffchange diffchange-inline"><b>YX</b> = <b>D</b> </del>&#8594; <b>110</b>,&nbsp;&nbsp;&nbsp;<del class="diffchange diffchange-inline"><b>YY</b> = <b>E</b> </del>&#8594; <b>1000</b>, <del class="diffchange diffchange-inline"><br></del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>: &nbsp; &nbsp; <ins class="diffchange diffchange-inline">$\rm </ins>XX = A<ins class="diffchange diffchange-inline">$ &nbsp; </ins>&#8594; &nbsp; <ins class="diffchange diffchange-inline">'''0''', </ins>&nbsp; &nbsp; <ins class="diffchange diffchange-inline"> $\rm </ins>XY = B<ins class="diffchange diffchange-inline">$ &nbsp; </ins>&#8594; &nbsp; <ins class="diffchange diffchange-inline">'''111''', </ins>&nbsp; &nbsp; <ins class="diffchange diffchange-inline"> $\rm </ins>XZ = C<ins class="diffchange diffchange-inline">$ &nbsp; </ins>&#8594<ins class="diffchange diffchange-inline">; &nbsp</ins>; <b>1011</b>, </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">: </del>&nbsp; &nbsp; <del class="diffchange diffchange-inline"><b></del>YZ<del class="diffchange diffchange-inline"></b> </del>= <del class="diffchange diffchange-inline"><b></del>F<del class="diffchange diffchange-inline"></b> </del>&#8594; <b>10010</b>,&nbsp;&nbsp;&nbsp; <del class="diffchange diffchange-inline"><b>ZX</b> = <b>G</b> </del>&#8594; <b>1010</b>,&nbsp;&nbsp;&nbsp;<del class="diffchange diffchange-inline"><b>ZY</b> = <b>H</b> </del>&#8594; <b>100111</b>,&nbsp;&nbsp;&nbsp;<del class="diffchange diffchange-inline"><b>ZZ</b> = <b>I</b> </del>&#8594; <b>100110</b> .</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">: </ins>&nbsp; &nbsp; <ins class="diffchange diffchange-inline"> $\rm YX = D$ </ins>&nbsp; &#8594<ins class="diffchange diffchange-inline">; &nbsp</ins>; <b>110</b>, &nbsp; &nbsp; <ins class="diffchange diffchange-inline"> $\rm YY = E$ </ins>&nbsp; &#8594<ins class="diffchange diffchange-inline">; &nbsp</ins>; <b>1000</b>, &nbsp; &nbsp; <ins class="diffchange diffchange-inline">$\rm </ins>YZ = F<ins class="diffchange diffchange-inline">$ &nbsp; </ins>&#8594<ins class="diffchange diffchange-inline">; &nbsp</ins>; <b>10010</b>,</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">: </ins>&nbsp; &nbsp; <ins class="diffchange diffchange-inline"> $\rm ZX = G$ </ins>&nbsp; &#8594<ins class="diffchange diffchange-inline">; &nbsp</ins>; <b>1010</b>, &nbsp; &nbsp; <ins class="diffchange diffchange-inline"> $\rm ZY = H$ </ins>&nbsp; &#8594<ins class="diffchange diffchange-inline">; &nbsp</ins>; <b>100111</b>, &nbsp; &nbsp; <ins class="diffchange diffchange-inline"> $\rm ZZ =I$ </ins>&nbsp; &#8594<ins class="diffchange diffchange-inline">; &nbsp</ins>; <b>100110</b>. <ins class="diffchange diffchange-inline"> </ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* für die mittlere Codewortlänge:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* für die mittlere Codewortlänge:</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:$$L_{\rm M}' =0.49 \cdot 1 + (0.14 + 0.14) \cdot 3 + (0.07 + 0.04 + 0.07) \cdot 4 + 0.02 \cdot 5 + (0.02 + 0.01) \cdot 6 = 2.33\,\,{\rm bit/Zweiertupel}$$</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:$$L_{\rm M<ins class="diffchange diffchange-inline">}\hspace{0.01cm</ins>}' =0.49 \cdot 1 + (0.14 + 0.14) \cdot 3 + (0.07 + 0.04 + 0.07) \cdot 4 + 0.02 \cdot 5 + (0.02 + 0.01) \cdot 6 = 2.33\,\,{\rm bit/Zweiertupel}$$</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:$$\Rightarrow\hspace{0.3cm}L_{\rm M} = {L_{\rm M}'}/{2}\hspace{0.15cm}\underline{ = 1.165\,\,{\rm bit/Quellensymbol}}\hspace{0.05cm}.$$</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:$$\Rightarrow\hspace{0.3cm}L_{\rm M} = {L_{\rm M<ins class="diffchange diffchange-inline">}\hspace{0.01cm</ins>}'}/{2}\hspace{0.15cm}\underline{ = 1.165\,\,{\rm bit/Quellensymbol}}\hspace{0.05cm}.$$</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''(4)'''&nbsp; Richtig ist <u>Aussage 1</u>, auch wenn <del class="diffchange diffchange-inline"><i>L</i><sub></del>M<del class="diffchange diffchange-inline"></sub> </del>mit wachsendem <del class="diffchange diffchange-inline"><i></del>k<del class="diffchange diffchange-inline"></i> </del>nur sehr langsam abfällt.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''(4)'''&nbsp; Richtig ist <ins class="diffchange diffchange-inline">die </ins><u>Aussage 1</u>, auch wenn <ins class="diffchange diffchange-inline">$L_{\rm </ins>M<ins class="diffchange diffchange-inline">}$ </ins>mit wachsendem <ins class="diffchange diffchange-inline">$</ins>k<ins class="diffchange diffchange-inline">$ </ins>nur sehr langsam abfällt.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Die letzte Aussage ist falsch, da <del class="diffchange diffchange-inline"><i>L</i><sub></del>M<del class="diffchange diffchange-inline"></sub> </del>auch für <del class="diffchange diffchange-inline"><i></del>k<del class="diffchange diffchange-inline"></i> </del>&#8594; &#8734; nicht kleiner sein kann als <del class="diffchange diffchange-inline"><i></del>H<del class="diffchange diffchange-inline"></i> </del>= 1.157 bit/Quellensymbol.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Die letzte Aussage ist falsch, da <ins class="diffchange diffchange-inline">$L_{\rm </ins>M<ins class="diffchange diffchange-inline">}$ </ins>auch für <ins class="diffchange diffchange-inline">$</ins>k &#8594; &#8734;<ins class="diffchange diffchange-inline">$ </ins>nicht kleiner sein kann als <ins class="diffchange diffchange-inline">$</ins>H = 1.157<ins class="diffchange diffchange-inline">$ </ins>bit/Quellensymbol.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Aber auch die zweite Aussage ist nicht unbedingt richtig: Da mit <del class="diffchange diffchange-inline"><i></del>k<del class="diffchange diffchange-inline"></i> </del>= 2 weiterhin <del class="diffchange diffchange-inline"><i>L</i><sub></del>M<del class="diffchange diffchange-inline"></sub> > <i</del>>H<del class="diffchange diffchange-inline"></i> </del>gilt, kann <del class="diffchange diffchange-inline"><i></del>k<del class="diffchange diffchange-inline"></i> </del>= 3 zu einer weiteren Verbesserung führen.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Aber auch die zweite Aussage ist nicht unbedingt richtig: <ins class="diffchange diffchange-inline">&nbsp; </ins>Da mit <ins class="diffchange diffchange-inline">$</ins>k = 2<ins class="diffchange diffchange-inline">$ </ins>weiterhin <ins class="diffchange diffchange-inline">$L_{\rm </ins>M<ins class="diffchange diffchange-inline">} </ins>> H<ins class="diffchange diffchange-inline">$ </ins>gilt, kann <ins class="diffchange diffchange-inline">$</ins>k = 3<ins class="diffchange diffchange-inline">$ </ins>zu einer weiteren Verbesserung führen.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{ML-Fuß}}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{ML-Fuß}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
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Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.7Z:_Huffman-Codierung_f%C3%BCr_Zweiertupel_einer_Tern%C3%A4rquelle&diff=26359&oldid=prev
Guenter am 28. September 2018 um 10:46 Uhr
2018-09-28T10:46:49Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 28. September 2018, 10:46 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l59" >Zeile 59:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Musterlösung===</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Musterlösung===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{ML-Kopf}}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{ML-Kopf}}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''(1)'''&nbsp; Die mittlere Codewortlänge ergibt sich mit <del class="diffchange diffchange-inline"><i>p</i><sub></del>X<del class="diffchange diffchange-inline"></sub> </del>= 0.7, <del class="diffchange diffchange-inline"><i>L</i><sub></del>X<del class="diffchange diffchange-inline"></sub> </del>= 1, <del class="diffchange diffchange-inline"><i>p</i><sub></del>Y<del class="diffchange diffchange-inline"></sub> </del>= 0.2, <del class="diffchange diffchange-inline"><i>L</i><sub></del>Y<del class="diffchange diffchange-inline"></sub> </del>= 2, <del class="diffchange diffchange-inline"><i>p</i><sub></del>Z<del class="diffchange diffchange-inline"></sub> </del>= 0.1, <del class="diffchange diffchange-inline"><i>L</i><sub></del>Z<del class="diffchange diffchange-inline"></sub> </del>= 2 zu</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''(1)'''&nbsp; Die mittlere Codewortlänge ergibt sich mit <ins class="diffchange diffchange-inline">&nbsp;$p_{\rm </ins>X<ins class="diffchange diffchange-inline">} </ins>= 0.7<ins class="diffchange diffchange-inline">$</ins>, <ins class="diffchange diffchange-inline">&nbsp;$L_{\rm </ins>X<ins class="diffchange diffchange-inline">} </ins>= 1<ins class="diffchange diffchange-inline">$</ins>, <ins class="diffchange diffchange-inline">&nbsp;$p_{\rm </ins>Y<ins class="diffchange diffchange-inline">} </ins>= 0.2<ins class="diffchange diffchange-inline">$</ins>, <ins class="diffchange diffchange-inline">&nbsp;$L_{\rm </ins>Y<ins class="diffchange diffchange-inline">} </ins>= 2<ins class="diffchange diffchange-inline">$</ins>, <ins class="diffchange diffchange-inline">&nbsp;$p_{\rm </ins>Z<ins class="diffchange diffchange-inline">} </ins>= 0.1<ins class="diffchange diffchange-inline">$</ins>, <ins class="diffchange diffchange-inline">&nbsp;$L_{\rm </ins>Z<ins class="diffchange diffchange-inline">} </ins>= 2<ins class="diffchange diffchange-inline">$ </ins>zu</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$L_{\rm M} = p_{\rm X} \cdot 1 + (p_{\rm Y} + p_{\rm Z}) \cdot 2 \hspace{0.15cm}\underline{= 1.3\,\,{\rm bit/Quellensymbol}}\hspace{0.05cm}. $$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$L_{\rm M} = p_{\rm X} \cdot 1 + (p_{\rm Y} + p_{\rm Z}) \cdot 2 \hspace{0.15cm}\underline{= 1.3\,\,{\rm bit/Quellensymbol}}\hspace{0.05cm}. $$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dieser Wert liegt noch deutlich über der Quellenentropie <i>H</i> = 1.157 bit/Quellensymbol.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dieser Wert liegt noch deutlich über der Quellenentropie <i>H</i> = 1.157 bit/Quellensymbol.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(2)'''&nbsp; Es gibt <i>M</i><sup>&nbsp;</sup>&prime; = <i>M</i><sup>&nbsp;2</sup> = 3<sup>2</sup> = 9 Zweiertupel mit folgenden Wahrscheinlichkeiten:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(2)'''&nbsp; Es gibt <i>M</i><sup>&nbsp;</sup>&prime; = <i>M</i><sup>&nbsp;2</sup> = 3<sup>2</sup> = 9 Zweiertupel mit folgenden Wahrscheinlichkeiten:</div></td></tr>
</table>
Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.7Z:_Huffman-Codierung_f%C3%BCr_Zweiertupel_einer_Tern%C3%A4rquelle&diff=26358&oldid=prev
Guenter am 28. September 2018 um 10:27 Uhr
2018-09-28T10:27:53Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 28. September 2018, 10:27 Uhr</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''Hinweise:'' </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''Hinweise:'' </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Die Aufgabe gehört zum Kapitel [[Informationstheorie/Entropiecodierung_nach_Huffman|Entropiecodierung nach Huffman]].</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Die Aufgabe gehört zum Kapitel [[Informationstheorie/Entropiecodierung_nach_Huffman|Entropiecodierung nach Huffman]].</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird auf die Seite [[Informationstheorie/Entropiecodierung_nach_Huffman#Anwendung_der_Huffman.E2.80.<del class="diffchange diffchange-inline">93Codierung_auf_k</del>.E2.80.93Tupel|Anwendung der Huffman-Codierung auf k-Tupel]] Bezug genommen.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird auf die Seite [[Informationstheorie/Entropiecodierung_nach_Huffman#Anwendung_der_Huffman.E2.80.<ins class="diffchange diffchange-inline">93Codierung_auf_.7F.27.22.60UNIQ-MathJax153-QINU.60.22.27.7F</ins>.E2.80.93Tupel|Anwendung der Huffman-Codierung auf k-Tupel]] Bezug genommen.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Eine vergleichbare Aufgabenstellung mit binären Eingangssymbolen wird in der [[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe 2.7]] behandelt.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Eine vergleichbare Aufgabenstellung mit binären Eingangssymbolen wird in der [[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe 2.7]] behandelt.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Bezeichnen Sie die möglichen Zweiertupel mit &nbsp; &nbsp; $\rm XX = A$,&nbsp;&nbsp;$\rm XY = B$,&nbsp;&nbsp;$\rm XZ = C$,&nbsp;&nbsp; $\rm YX = D$,&nbsp;&nbsp;$\rm YY = E$,&nbsp;&nbsp;$\rm YZ = F$,&nbsp;&nbsp;$\rm ZX = G$,&nbsp;&nbsp;$\rm ZY = H$,&nbsp;&nbsp;$\rm ZZ = I$.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Bezeichnen Sie die möglichen Zweiertupel mit &nbsp; &nbsp; $\rm XX = A$,&nbsp;&nbsp;$\rm XY = B$,&nbsp;&nbsp;$\rm XZ = C$,&nbsp;&nbsp; $\rm YX = D$,&nbsp;&nbsp;$\rm YY = E$,&nbsp;&nbsp;$\rm YZ = F$,&nbsp;&nbsp;$\rm ZX = G$,&nbsp;&nbsp;$\rm ZY = H$,&nbsp;&nbsp;$\rm ZZ = I$.</div></td></tr>
</table>
Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.7Z:_Huffman-Codierung_f%C3%BCr_Zweiertupel_einer_Tern%C3%A4rquelle&diff=26357&oldid=prev
Guenter am 28. September 2018 um 10:26 Uhr
2018-09-28T10:26:39Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 28. September 2018, 10:26 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3" >Zeile 3:</td>
<td colspan="2" class="diff-lineno">Zeile 3:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:P_ID2458__Inf_Z_2_7.png|right|Huffman–Baum für Ternärquelle]]</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:P_ID2458__Inf_Z_2_7.png|right<ins class="diffchange diffchange-inline">|frame</ins>|Huffman–Baum für Ternärquelle]]</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Wir betrachten den gleichen Sachverhalt wie in der [[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe A2.7]]: Der Huffman&ndash;Algorithmus führt zu einem besseren Ergebnis, das heißt zu einer kleineren mittleren Codewortlänge $L_{\rm M}$, wenn man ihn nicht auf einzelne Symbole anwendet, sondern vorher $k$&ndash;Tupel bildet. Dadurch erhöht man den Symbolumfang von $M$ auf $M' = M^k$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Wir betrachten den gleichen Sachverhalt wie in der [[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe A2.7]]: <ins class="diffchange diffchange-inline">&nbsp; </ins>Der Huffman&ndash;Algorithmus führt zu einem besseren Ergebnis, das heißt zu einer kleineren mittleren Codewortlänge $L_{\rm M}$, wenn man ihn nicht auf einzelne Symbole anwendet, sondern vorher $k$&ndash;Tupel bildet. Dadurch erhöht man den Symbolumfang von $M$ auf $M' = M^k$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Für die hier betrachtete Nachrichtenquelle gilt:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Für die hier betrachtete Nachrichtenquelle gilt:</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Symbolumfang: $M = 3$,</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Symbolumfang: <ins class="diffchange diffchange-inline">&nbsp; </ins>$M = 3$,</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Symbolvorrat: $\{$<del class="diffchange diffchange-inline"><b></del>X<del class="diffchange diffchange-inline"></b></del>, <del class="diffchange diffchange-inline"><b></del>Y<del class="diffchange diffchange-inline"></b></del>, <del class="diffchange diffchange-inline"><b></del>Z<del class="diffchange diffchange-inline"></b></del>$\}$,</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Symbolvorrat: <ins class="diffchange diffchange-inline">&nbsp; </ins>$\{$ <ins class="diffchange diffchange-inline">$\rm </ins>X<ins class="diffchange diffchange-inline">$</ins>, <ins class="diffchange diffchange-inline">$\rm </ins>Y<ins class="diffchange diffchange-inline">$</ins>, <ins class="diffchange diffchange-inline">$\rm </ins>Z<ins class="diffchange diffchange-inline">$ </ins>$\}$,</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Wahrscheinlichkeiten: $p_{\rm X} = 0.7$, $p_{\rm Y} = 0.2$, $p_{\rm Z} = 0.1$,</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Wahrscheinlichkeiten: <ins class="diffchange diffchange-inline">&nbsp; </ins>$p_{\rm X} = 0.7$, $p_{\rm Y} = 0.2$, $p_{\rm Z} = 0.1$,</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Entropie: $H = 1.157 \ \rm bit/Ternärsymbol$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Entropie: <ins class="diffchange diffchange-inline">&nbsp; </ins>$H = 1.157 \ \rm bit/Ternärsymbol$.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Die Grafik zeigt den Huffman&ndash;Baum, wenn man den Huffman&ndash;Algorithmus auf Einzelsymbole anwendet, also den Fall $k= 1$. In der Teilaufgabe '''(2)''' sollen Sie den entsprechenden Huffman&ndash;Code angeben, wenn vorher Zweiertupel gebildet werden $(k=2)$.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Die Grafik zeigt den Huffman&ndash;Baum, wenn man den Huffman&ndash;Algorithmus auf Einzelsymbole anwendet, also den Fall $k= 1$. In der Teilaufgabe (2) sollen Sie den entsprechenden Huffman&ndash;Code angeben, wenn vorher Zweiertupel gebildet werden ($k=2$).</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l20" >Zeile 20:</td>
<td colspan="2" class="diff-lineno">Zeile 23:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird auf die Seite [[Informationstheorie/Entropiecodierung_nach_Huffman#Anwendung_der_Huffman.E2.80.93Codierung_auf_k.E2.80.93Tupel|Anwendung der Huffman-Codierung auf k-Tupel]] Bezug genommen.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird auf die Seite [[Informationstheorie/Entropiecodierung_nach_Huffman#Anwendung_der_Huffman.E2.80.93Codierung_auf_k.E2.80.93Tupel|Anwendung der Huffman-Codierung auf k-Tupel]] Bezug genommen.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Eine vergleichbare Aufgabenstellung mit binären Eingangssymbolen wird in der [[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe 2.7]] behandelt.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Eine vergleichbare Aufgabenstellung mit binären Eingangssymbolen wird in der [[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe 2.7]] behandelt.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Bezeichnen Sie die möglichen Zweiertupel mit &nbsp; &nbsp; <del class="diffchange diffchange-inline"><b></del>XX<del class="diffchange diffchange-inline"></b> </del>= <del class="diffchange diffchange-inline"><b></del>A<del class="diffchange diffchange-inline"></b></del>,&nbsp;&nbsp;<del class="diffchange diffchange-inline"><b></del>XY<del class="diffchange diffchange-inline"></b> </del>= <del class="diffchange diffchange-inline"><b></del>B<del class="diffchange diffchange-inline"></b></del>,&nbsp;&nbsp;<del class="diffchange diffchange-inline"><b></del>XZ<del class="diffchange diffchange-inline"></b> </del>= <del class="diffchange diffchange-inline"><b></del>C<del class="diffchange diffchange-inline"></b></del>,&nbsp;&nbsp; <del class="diffchange diffchange-inline"><b></del>YX<del class="diffchange diffchange-inline"></b> </del>= <del class="diffchange diffchange-inline"><b></del>D<del class="diffchange diffchange-inline"></b></del>,&nbsp;&nbsp;<del class="diffchange diffchange-inline"><b></del>YY<del class="diffchange diffchange-inline"></b> </del>= <del class="diffchange diffchange-inline"><b></del>E<del class="diffchange diffchange-inline"></b></del>,&nbsp;&nbsp;<del class="diffchange diffchange-inline"><b></del>YZ<del class="diffchange diffchange-inline"></b> </del>= <del class="diffchange diffchange-inline"><b></del>F<del class="diffchange diffchange-inline"></b></del>,&nbsp;&nbsp;<del class="diffchange diffchange-inline"><b></del>ZX<del class="diffchange diffchange-inline"></b> </del>= <del class="diffchange diffchange-inline"><b></del>G<del class="diffchange diffchange-inline"></b></del>,&nbsp;&nbsp;<del class="diffchange diffchange-inline"><b></del>ZY<del class="diffchange diffchange-inline"></b> </del>= <del class="diffchange diffchange-inline"><b></del>H<del class="diffchange diffchange-inline"></b></del>,&nbsp;&nbsp;<del class="diffchange diffchange-inline"><b></del>ZZ<del class="diffchange diffchange-inline"></b> </del>= <del class="diffchange diffchange-inline"><b></del>I<del class="diffchange diffchange-inline"></b> </del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Bezeichnen Sie die möglichen Zweiertupel mit &nbsp; &nbsp; <ins class="diffchange diffchange-inline">$\rm </ins>XX = A<ins class="diffchange diffchange-inline">$</ins>,&nbsp;&nbsp;<ins class="diffchange diffchange-inline">$\rm </ins>XY = B<ins class="diffchange diffchange-inline">$</ins>,&nbsp;&nbsp;<ins class="diffchange diffchange-inline">$\rm </ins>XZ = C<ins class="diffchange diffchange-inline">$</ins>,&nbsp;&nbsp; <ins class="diffchange diffchange-inline">$\rm </ins>YX = D<ins class="diffchange diffchange-inline">$</ins>,&nbsp;&nbsp;<ins class="diffchange diffchange-inline">$\rm </ins>YY = E<ins class="diffchange diffchange-inline">$</ins>,&nbsp;&nbsp;<ins class="diffchange diffchange-inline">$\rm </ins>YZ = F<ins class="diffchange diffchange-inline">$</ins>,&nbsp;&nbsp;<ins class="diffchange diffchange-inline">$\rm </ins>ZX = G<ins class="diffchange diffchange-inline">$</ins>,&nbsp;&nbsp;<ins class="diffchange diffchange-inline">$\rm </ins>ZY = H<ins class="diffchange diffchange-inline">$</ins>,&nbsp;&nbsp;<ins class="diffchange diffchange-inline">$\rm </ins>ZZ = I<ins class="diffchange diffchange-inline">$</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l27" >Zeile 27:</td>
<td colspan="2" class="diff-lineno">Zeile 30:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><quiz display=simple></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><quiz display=simple></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Wie groß ist die mittlere Codewortlänge, wenn der Huffman&ndash;Algorithmus direkt auf die ternären Quellensymbole <del class="diffchange diffchange-inline"><b></del>X<del class="diffchange diffchange-inline"></b></del>, <del class="diffchange diffchange-inline"><b></del>Y<del class="diffchange diffchange-inline"></b> </del>und <del class="diffchange diffchange-inline"><b></del>Z<del class="diffchange diffchange-inline"></b> </del>angewendet wird?</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Wie groß ist die mittlere Codewortlänge, wenn der Huffman&ndash;Algorithmus direkt auf die ternären Quellensymbole <ins class="diffchange diffchange-inline">$\rm </ins>X<ins class="diffchange diffchange-inline">$</ins>, <ins class="diffchange diffchange-inline">$\rm </ins>Y<ins class="diffchange diffchange-inline">$ </ins>und <ins class="diffchange diffchange-inline">$\rm </ins>Z<ins class="diffchange diffchange-inline">$ </ins>angewendet wird? </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$k= 1\text{:} \hspace{0.25cm}L_{\rm M} \ = \ $ { 1.3 3% } $\ \rm bit/Quellensymbol$</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$<ins class="diffchange diffchange-inline">\underline{</ins>k=1<ins class="diffchange diffchange-inline">}</ins>\text{:} \hspace{0.25cm}L_{\rm M} \ = \ $ { 1.3 3% } $\ \rm bit/Quellensymbol$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Wie groß sind die Tupel&ndash;Wahrscheinlichkeiten? Insbesondere:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Wie groß sind die Tupel&ndash;Wahrscheinlichkeiten? Insbesondere:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm A} = <del class="diffchange diffchange-inline">{</del>\rm Pr<del class="diffchange diffchange-inline">}</del>(<del class="diffchange diffchange-inline">$'''</del>XX<del class="diffchange diffchange-inline">'''$</del>)\ = \ $ { 0.49 3% }</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm A} = \rm Pr(XX)\ = \ $ { 0.49 3% }</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm B} = <del class="diffchange diffchange-inline">{</del>\rm Pr<del class="diffchange diffchange-inline">}</del>(<del class="diffchange diffchange-inline">$'''</del>XY<del class="diffchange diffchange-inline">'''$</del>)\ = \ $ { 0.14 3% }</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm B} = \rm Pr(XY)\ = \ $ { 0.14 3% }</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm C} = <del class="diffchange diffchange-inline">{</del>\rm Pr<del class="diffchange diffchange-inline">}</del>(<del class="diffchange diffchange-inline">$'''</del>XZ<del class="diffchange diffchange-inline">'''$</del>)\ = \ $ { 0.07 3% }</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm C} = \rm Pr(XZ)\ = \ $ { 0.07 3% }</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Wie groß ist die mittlere Codewortlänge, wenn man zuerst Zweiertupel bildet und darauf den Huffman&ndash;Algorithmus anwendet?</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Wie groß ist die mittlere Codewortlänge, wenn man zuerst Zweiertupel bildet und darauf den Huffman&ndash;Algorithmus anwendet?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$k= 2\text{:} \hspace{0.25cm}L_{\rm M} \ = \ $ { 1.165 3% } $\ \rm bit/Quellensymbol$</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$<ins class="diffchange diffchange-inline">\underline{</ins>k=2<ins class="diffchange diffchange-inline">}</ins>\text{:} \hspace{0.25cm}L_{\rm M} \ = \ $ { 1.165 3% } $\ \rm bit/Quellensymbol$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Welche der folgenden Aussagen sind zutreffend, wenn man mehr als zwei Ternärzeichen zusammenfasst ($k>2$)?</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Welche der folgenden Aussagen sind zutreffend, wenn man mehr als zwei Ternärzeichen zusammenfasst ($k>2$)?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="[]"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="[]"}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>+ $L_{\rm M}$ fällt monoton mit steigendem $k$ ab.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>+ $L_{\rm M}$<ins class="diffchange diffchange-inline">&nbsp; </ins>fällt monoton mit steigendem <ins class="diffchange diffchange-inline">&nbsp;</ins>$k$<ins class="diffchange diffchange-inline">&nbsp; </ins>ab.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>- $L_{\rm M} $ändert sich nicht, wenn man $k$ erhöht.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>- $L_{\rm M}$<ins class="diffchange diffchange-inline">&nbsp; </ins>ändert sich nicht, wenn man <ins class="diffchange diffchange-inline">&nbsp;</ins>$k$<ins class="diffchange diffchange-inline">&nbsp; </ins>erhöht.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>- Für $k= 3$ erhält man $L_{\rm M} = 1.05 \ \rm bit/Quellensymbol$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>- Für <ins class="diffchange diffchange-inline">&nbsp;</ins>$k= 3$<ins class="diffchange diffchange-inline">&nbsp; </ins>erhält man <ins class="diffchange diffchange-inline">&nbsp;</ins>$L_{\rm M} = 1.05 \ \rm bit/Quellensymbol$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>
Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.7Z:_Huffman-Codierung_f%C3%BCr_Zweiertupel_einer_Tern%C3%A4rquelle&diff=24866&oldid=prev
Mwiki-lnt: Textersetzung - „*Sollte die Eingabe des Zahlenwertes „0” erforderlich sein, so geben Sie bitte „0.” ein.“ durch „ “
2018-05-29T12:02:46Z
<p>Textersetzung - „*Sollte die Eingabe des Zahlenwertes „0” erforderlich sein, so geben Sie bitte „0.” ein.“ durch „ “</p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 29. Mai 2018, 12:02 Uhr</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Eine vergleichbare Aufgabenstellung mit binären Eingangssymbolen wird in der [[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe 2.7]] behandelt.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Eine vergleichbare Aufgabenstellung mit binären Eingangssymbolen wird in der [[Aufgaben:2.7_Huffman-Anwendung_für_binäre_Zweiertupel|Aufgabe 2.7]] behandelt.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Bezeichnen Sie die möglichen Zweiertupel mit &nbsp; &nbsp; <b>XX</b> = <b>A</b>,&nbsp;&nbsp;<b>XY</b> = <b>B</b>,&nbsp;&nbsp;<b>XZ</b> = <b>C</b>,&nbsp;&nbsp; <b>YX</b> = <b>D</b>,&nbsp;&nbsp;<b>YY</b> = <b>E</b>,&nbsp;&nbsp;<b>YZ</b> = <b>F</b>,&nbsp;&nbsp;<b>ZX</b> = <b>G</b>,&nbsp;&nbsp;<b>ZY</b> = <b>H</b>,&nbsp;&nbsp;<b>ZZ</b> = <b>I</b> .</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Bezeichnen Sie die möglichen Zweiertupel mit &nbsp; &nbsp; <b>XX</b> = <b>A</b>,&nbsp;&nbsp;<b>XY</b> = <b>B</b>,&nbsp;&nbsp;<b>XZ</b> = <b>C</b>,&nbsp;&nbsp; <b>YX</b> = <b>D</b>,&nbsp;&nbsp;<b>YY</b> = <b>E</b>,&nbsp;&nbsp;<b>YZ</b> = <b>F</b>,&nbsp;&nbsp;<b>ZX</b> = <b>G</b>,&nbsp;&nbsp;<b>ZY</b> = <b>H</b>,&nbsp;&nbsp;<b>ZZ</b> = <b>I</b> .</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">*Sollte die Eingabe des Zahlenwertes &bdquo;0&rdquo; erforderlich sein, so geben Sie bitte &bdquo;0.&rdquo; ein.</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> </ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
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Mwiki-lnt
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.7Z:_Huffman-Codierung_f%C3%BCr_Zweiertupel_einer_Tern%C3%A4rquelle&diff=21831&oldid=prev
Guenter: Guenter verschob die Seite Aufgaben:2.7Z Huffman-Codierung für Zweiertupel einer Ternärquelle nach Aufgaben:Aufgabe 2.7Z: Huffman-Codierung für Zweiertupel einer Ternärquelle
2018-01-03T14:00:03Z
<p>Guenter verschob die Seite <a href="/Aufgaben:2.7Z_Huffman-Codierung_f%C3%BCr_Zweiertupel_einer_Tern%C3%A4rquelle" class="mw-redirect" title="Aufgaben:2.7Z Huffman-Codierung für Zweiertupel einer Ternärquelle">2.7Z Huffman-Codierung für Zweiertupel einer Ternärquelle</a> nach <a href="/Aufgaben:Aufgabe_2.7Z:_Huffman-Codierung_f%C3%BCr_Zweiertupel_einer_Tern%C3%A4rquelle" title="Aufgaben:Aufgabe 2.7Z: Huffman-Codierung für Zweiertupel einer Ternärquelle">Aufgabe 2.7Z: Huffman-Codierung für Zweiertupel einer Ternärquelle</a></p>
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<td colspan="1" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="1" style="background-color: #fff; color: #222; text-align: center;">Version vom 3. Januar 2018, 14:00 Uhr</td>
</tr><tr><td colspan="2" class="diff-notice" lang="de"><div class="mw-diff-empty">(kein Unterschied)</div>
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Guenter