Response to the following problem:
A discrete-time zero-mean Gaussian random process has a variance per sample of σ21 . This source generates outputs at a rate of 1000 per second. The samples are transmitted over a discrete-time AWGN channel with input power constraint of P and noise variance per sample of σ2 2 . This channel is capable of transmitting 500 symbols per second.
1. If the source is to be transmitted over the channel, you are allowed to employ processing schemes of any degree of complexity, and any delay is acceptable, what is the minimum achievable distortion per sample?
2. If the channel remains the same but you have to use binary antipodal signals at the input and employ hard decision decoding at the output (again no limit on complexity and delay), what is the minimum achievable distortion per sample?
3. Now assume that the source has the same statistics but is not memory less. Comparing with part 1, do you expect the distortion to decrease or increase? Give your answer in a short paragraph.