Design the 1st order, 2nd order, and 1st order conditional Huffman codes for this source. Calculate the resulting bit rate for each case. Compare it to the corresponding lower and upper bounds defined by the entropy

N 8.6 A Markov source with three symbols A = {az, az, az} has the following proba- bility distributions: p(a) = 5; i = 1, 2, 3, P{ai/aj) = otherwise. (a) Calculate the first of this source. (b) Design the first-order, second-order, and first-order conditional Huffman codes for this source. Calculate the resulting bit rate for each case. Compare it to the corresponding lower and upper bounds defined by the entropy. (C) What is the minimal bit rate achievable with this achien N 8.6 A Markov source with three symbols A = {az, az, az} has the following proba- bility distributions: p(a) = 5; i = 1, 2, 3, P{ai/aj) = otherwise. (a) Calculate the first of this source. (b) Design the first-order, second-order, and first-order conditional Huffman codes for this source. Calculate the resulting bit rate for each case. Compare it to the corresponding lower and upper bounds defined by the entropy. (C) What is the minimal bit rate achievable with this achien