Solve the following problem:
Consider the channel model shown in Figure . Assume that the top channel is a noiseless BSC channel for which crossover probability is zero and the bottom channel is a binary-input binary-output Z channel with P [Y = 1 |X = 1 ] = 1 and P [Y = 0 |X = 0 ] = ½. The channel switches between the two states independently for each transmission, and the two states are equiprobable.
1. Determine the ergodic capacity of this channel when no state information is available.
2. Determine the ergodic capacity of the channel when perfect state information is available at both sides.
3. Determine the ergodic capacity of the channel when perfect state information is available at the receiver.
