Processing math: 100%

0,0

$p_\mathrm{A} =$

0.1

$\Rightarrow p_\mathrm{B} =$

0.9

$p_\mathrm{b|A} =$

0.05

$\Rightarrow p_\mathrm{a|A} =$

0.95

$p_\mathrm{a|B} =$

0.4

$\Rightarrow p_\mathrm{b|B} =$

0.6

$p_\mathrm{A} =$

0.4

$p_\mathrm{B} =$

0.3

$\Rightarrow p_\mathrm{C} =$

0.3

$p_\mathrm{b|A} =$

0.5

$p_\mathrm{c|A} =$

$\Rightarrow p_\mathrm{a|A} =$

0.5

$p_\mathrm{a|B} =$

0.5

$p_\mathrm{c|B} =$

$\Rightarrow p_\mathrm{b|B} =$

0.5

$p_\mathrm{a|C} =$

0.5

$p_\mathrm{b|C} =$

0.5

$\Rightarrow p_\mathrm{c|C} =$

Binary source

Symbol probabilities

Transition probabilities

algebraic simulative

$N=$ binary ternary

0,0

Exemplary source symbol sequence

$\langle \hspace{0.05cm} X_n\hspace{0.05cm} \rangle$

Exemplary sink symbol sequence

$\langle \hspace{0.05cm} Y_n\hspace{0.05cm} \rangle$

$H(XY) =$

Gerichtete Darstellung.

$H(X)$

$H(Y)$

$H(X|Y)$

$H(Y|X)$

$I(X;Y)$

Results of the analytical calculation for the binary channel

BBBBBBBBBBBBBBABBBBBBBABBBBBBBBBBBBBBBBB
BBBBBBBBBBBBBBABBBABAABBABBABBBABBABABBB
BBBBBBBBBBBBBBBBBBBABBBBBBBBBBBBBBBBABBB
BBBBBBBBBBABBBBBBBBBABBABBBBBBAABBBBBBBB
BBBBABABBBBBBBBBBBBBBBBBBBBBBBBBBBBABBBB

babbaababaababaaababbaabbbbbabbbabbbbaab
abbbbbbabaabaaaabbabaabbbbaabbbabbaaaaab
abaabaabbabaaabbbbbabbbaaabbbbababbbabba
aababbbaaabbabaabbbaabbababbbaaababbaaab
bbbbaaababaabbbbbabaabbabaababaabaaabbbb

1.371
0.469		0.902
0.377	0.994
0.377	0.092	0.902

0.469

0.377

0.092

0.994

0.902

0,0

Composite probabilities

$\mathrm{Pr}(X \cap Y)$

Conditional probabilities

$\mathrm{Pr}(Y | X)$

Inference probabilities

$\mathrm{Pr}(X | Y)$

	a	b
A	0.095	0.005
B	0.36	0.54

	a	b
A	0.95	0.05
B	0.4	0.6

	a	b
A	0.2088	0.0092
B	0.7912	0.9908

* First, select the number $(1,\ 2, \text{...} \ )$ of the task to be processed. The number " $0$ " corresponds to a "Reset": Same setting as at program start.
* A task description is displayed. The parameter values are adjusted. Solution after pressing "Show Solution".
* Source symbols are denoted by uppercase letters (binary: $\rm A$ , $\rm B$ ), sink symbols by lowercase letters ( $\rm a$ , $\rm b$ ). Error-free transmission: $\rm A \rightarrow a$ .
* For all entropy values, the unit "bit/use" would have to be added.

Capacity of Memoryless Digital Channels