In transmitting a bit from location A to location B, if we let X denote the value of the b...

In transmitting a bit from location A to location B, if we let X denote the value of the bit sent at location A and Y denote the value received at location B, then H(X) – HY(X) is called the rate of transmission of information from A to B. The maximal rate of transmission, as a function of P{X = 1}= 1- P{X =0}, is called the channel capacity. Show that for a binary symmetric channel with P{Y = 1|X = 1} = P{Y = 0|X = 0} = p, the channel capacity is attained by the rate of transmission of information when P{X = 1} =  and its value is 1 + p log p + (1 - p) log(l - p).