Assuming that a gaussian source with variance sigma2 1 is

Question

A communication channel is shown in Figure P6.47.

1. Show that, regardless of the contents of the probability transition matrix of the channel, we have

2. Determine one probability transition matrix under which the above upper bound is achieved.

3. Assuming that a Gaussian source with variance σ² = 1 is to be transmitted via the channel in part 2, what is the minimum achievable distortion? (Mean squared distortion is assumed throughout.)