Response to the following problem:
Each sample of a Gaussian memory less source has a variance equal to 4, and the source produces 8000 samples per second. The source is to be transmitted via an additive white Gaussian noise channel with a bandwidth equal to 4000 Hz, and it is desirable to have a distortion per sample not exceeding 1 at the destination (assume squared-error distortion).
1. What is the minimum required signal-to-noise ratio of the channel?
2. If it is further assumed that, on the same channel, a BPSK scheme is employed with hard decision decoding, what will be the minimum required channel signal-to-noise ratio?
Note: the signal-to-noise ratio of the channel is defined by P/NoW .