Mismatched Decoding Revisited: General Alphabets, Channels with Memory, and the Wide-Band Limit

The mismatch capacity of a channel is the highest rate at which reliable communication is possible over the channel with a given (possibly sub-optimal) decoding rule. This quantity has been studied extensively for single-letter decoding rules over discrete memoryless channels. Here, we extend the study to memoryless channels with general alphabets and to channels with memory with possibly non single-letter decoding rules. We also study the wide-band limit, and in particular the mismatch capacity per unit cost, and the mismatch capacity of spread-spectrum systems.