The likelihood decoder: Error exponents and mismatch

This paper studies likelihood decoding for channel coding over discrete memoryless channels. It is shown that the likelihood decoder recovers the same random-coding error exponents as the maximum-likelihood decoder for i.i.d. and constant-composition random codes. The role of mismatch in likelihood decoding is studied, and the notion of the mismatched likelihood decoder capacity is introduced. It is shown, both in the case of random coding and optimized codebooks, that the mismatched likelihood decoder can lead to strictly worse achievable rates and error exponents compared to the corresponding mismatched maximum-metric decoder.