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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. 1
  2. -plog(p)-(1-p)log(1-p)
  3. 1+plog(p)+(1-p)log(1-p)
  4. 0
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Ans  is B:  -plog(p)-(1-p)log(1-p)

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