Response to the following problem:
Figure illustrates a binary erasure channel with transition probabilities P(0|0) = P(1|1) = 1 - p and P(e|0) = P(e|1) = p. The probabilities for the input symbols are P(X = 0) = α and P(X = 1) = 1 - α.
1. Determine the average mutual information I(X; Y ) in bits.
2. Determine the value of α that maximizes I(X; Y ), i.e., the channel capacity C in bits per channel use, and plot C as a function of p for the optimum value of α.
3. For the value of α found in part 2, determine the mutual information I(x; y) = I(0; 0), I(1; 1), I(0; e), and I(1; e), where
