Consider the conditional entropy and mutual information for the binary symmetric channel. The input source has alphabet $X=\{0,1\}$ and associated probabilities ${\frac{1}{2}, \frac{1}{2}}$. The channel matrix is $\begin{pmatrix} 1-p & p \\ p & 1-p \end{pmatrix}$ wgere p is the transition probability. Then the conditional entropy is given by:
- 1
- -plog(p)-(1-p)log(1-p)
- 1+plog(p)+(1-p)log(1-p)
- 0