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Achievable and converse bounds for general channels and mismatched decodingare derived. The direct (achievable) bound is derived using random coding andthe analysis is tight up to factor 2. The converse is given in term of theachievable bound and the factor between them is given. This gives performanceof the best rate-R code with possible mismatched decoding metric over a generalchannel, up to the factor that is identified. In the matched case we show thatthe converse equals the minimax meta-converse of Polyanskiy et al.

Achievable and Converse bounds over a general channel and general decoding metric