Ensemble-tight error exponents for mismatched decoders

This paper studies channel coding for discrete memoryless channels with a given (possibly suboptimal) decoding rule. Using upper and lower bounds on the random-coding error probability, the exponential behavior of three random-coding ensembles is characterized. The ensemble tightness of existing achievable error exponents is proven for the i.i.d. and constant-composition ensembles, and a new ensemble-tight error exponent is given for the cost-constrained i.i.d. ensemble. Connections are drawn between the ensembles under both mismatched decoding and maximum-likelihood decoding.