Consider the source AS = {a, b, c, d, e}, PS = {1/3, 1/3, 1/9, 1/9, 1/9} and the channel whose transition probability matrix is

Note that the source alphabet has five symbols, but the channel alphabet A_X = A_Y = {0, 1, 2, 3} has only four. Assume that the source produces symbols at exactly 3/4 the rate that the channel accepts channel symbols. For a given (tiny) > 0, explain how you would design a system for communicating the source's output over the channel with an average error probability per source symbol less than . Be as explicit as possible. In particular, do not invoke Shannon's noisy-channel coding theorem.