We consider transmission over a discrete memoryless channel (DMC) W(y\x) with finite alphabets X and Y. It is assumed that an (n, Mn)-codebook Mn = [x1,..., xMn} with rate Rn = 1/n log Mn is used for transmission. The type-dependent maximum-metric decoder estimates the transmitted message as m = arg maxxiMn q(Pxi, y), (1) where xy is the joint empirical distribution [1, Ch. 2] of the pair (x, y) and the metric q : P(X × Y) → R is continuous. Maximum-likelihood (ML) decoding is a special case of (1), but the decoder may in general be mismatched [2], [3]
