Solve the following problem:
A discrete-time memory less Gaussian source with mean 0 and variance σ2 is to be transmitted over a binary symmetric channel with crossover probability ε.
1. What is the minimum value of the distortion attainable at destination? (Distortion is measured in mean squared error.)
2. If the channel is discrete-time memory less additive Gaussian noise with input power P and noise power σ2n , what is the minimum attainable distortion?
3. Now assume that the source has the same basic properties but is not memory less. Do you expect that the distortion in transmission over the binary symmetric channel to be decreased or increased? Why?