Consider the following lossy compression scheme for binary sequences. We divide the binary sequence into blocks of size M. For each block we count the number of Os. If this number is greater than or equal to M/2, we send a 0; otherwise, we send a 1.
(a) If the sequence is random with P(0) = 0.8, compute the rate and distortion for M = 1, 2,4, 8, 16. Compare your results with the rate distortion function for binary sources.
(b) Repeat assuming that the output of the encoder is encoded at a rate equal to the entropy of the output.