Mismatched decoding: DMC and general channels

The setup of mismatched decoding is considered. By analyzing multi-letter expressions and bounds on the mismatch capacity of a general channel, several results pertaining to the mismatched discrete memoryless channel W with an additive metric q are deduced: it is shown that Csiszár and Narayan's “product-space" improvement of the random coding lower bound on the mismatched capacity, C (∞) q (W), is equal to the mismatched threshold capacity with a constant threshold level. It is also proved that C (∞) q (W) is the highest rate achievable when the average probability of error converges to zero at a certain specified rate, which is o(1/n) in the case of q which is a bounded rational metric. Finally a lower bound on the average probability of error at rates above the erasures-only capacity of the DMC is derived.