(a) Given a binary channel shown in Figure (i) Find the channel matri…

Previous year question for Information Theory and Coding.

Question

(a) Given a binary channel shown in Figure

(i) Find the channel matrix of the channel

(ii) Find $P(y_1)$ and $P(Y_2)$ when $P(x_1) = P(x_2) = 0.5$

(iii) Find joint probability $P(x_1, y_2)$ and $P(x_2, y_1)$ when $P(x_1) = P(x_2) = 0.5$

(b) Find the channel capacity of the binary erasure channel.