Determine the map decoding region for the codeword

Question

Assignment:

A ternary memoryless channel has input and output alphabet A_c = Ac¯ = {1,2,3}, symbol period Tc = 100 ns and transition probabilities

Pc|c(ξ|y) = {1/y, ξ ≤ y 0, ξ > y

a) Find the probability P [c¯≠ c] for three-symbol words when the input message {c} has iid symbols with equally likely values.

b) Show the MAP decoding region for the codeword [222] in the code C = {111, 222, 333} with equally likely codewords.