申論題

4. (Total-18%) Consider a binary symmetric channel with input X, output Y, and transition probability a. More specifically, as shown in the figure below, the input and output of the channel may be "0" or "1", P(Y=0|X=0)= P(Y = 1|X = 1) = 1 - a and P(Y = 1|X = 0) = P(Y=0|X=0) = a. The prior probability is P(X = 0) = p.

(a) (4%) Find the entropy H(Y) and the conditional entropy H(Y|X).