Information Theory and Coding I - Exercises 7 9 Rate Distortion Assume a source Q {0,1,2} defined by Po(0) = 1/2, P2(1) = Po(2) = 1/4. The output alphabet is given by {0,1,2}. The distortion is calculated by d(9, ) = 19 - 91 1. Calculate HQ) and give the minimal rate for lossless source coding, R(0) 2. Determine an average distortion Dmax, where the rate approaches 0. 3. Determine the average distortion, D, and the mutual information I(Q;0), for a) input symbol 0 is merged with symbol 1 b) input symbol 2 is merged with symbol o c) input symbol 2 is merged with symbol 1 Information Theory and Coding I - Exercises 7 9 Rate Distortion Assume a source Q {0,1,2} defined by Po(0) = 1/2, P2(1) = Po(2) = 1/4. The output alphabet is given by {0,1,2}. The distortion is calculated by d(9, ) = 19 - 91 1. Calculate HQ) and give the minimal rate for lossless source coding, R(0) 2. Determine an average distortion Dmax, where the rate approaches 0. 3. Determine the average distortion, D, and the mutual information I(Q;0), for a) input symbol 0 is merged with symbol 1 b) input symbol 2 is merged with symbol o c) input symbol 2 is merged with symbol 1