# Consider the binary symmetric channel described in Figure.

# Consider the binary symmetric channel described in Figure.

Consider the binary symmetric channel described in Figure. Let Po denote the prob. ability of sending binary symbol x0 = 0, and let p1 = 1 â P0 denote the probability of sending binary symbol x1 = 1, Let p denote the transition probability of the channel

(a) Show that the mutual information between the channel input and channel output is given by

(b) Show that the value of p0 that maximizes I{X; Y) is equal to 1/2.

(c) Hence, show that the channel capacity equals. C = 1 âH(p)