ON INFORMATION RATES FOR MISMATCHED DECODERS

Reliable transmission over a discrete-time memoryless channel with a d ecoding metric that is not necessarily matched to the channel (mismatc hed decoding) is considered. It is assumed that the encoder knows both the true channel and the decoding metric. The lower bound on the high est achievable rate found by Csiszar and Korner and by Hui for DMC's, hereafter denoted C(LM), is shown to bear some interesting information -theoretic meanings. The bound C(LM) turns out to be the highest achie vable rate in the random coding sense, namely, the random coding capac ity for mismatched decoding. It is also demonstrated that the epsilon- capacity associated with mismatched decoding cannot exceed C(LM). New bounds and some properties of C(LM) are established and used to find r elations to the generalized mutual information and to the generalized cutoff rate. The expression for C(LM) is extended to a certain class o f memoryless channels with continuous input and output alphabets, and is used to calculate C(LM) explicitly for several examples of theoreti cal and practical interest. Finally, it is demonstrated that in contra st to the classical matched decoding case, here, under the mismatched decoding regime, the highest achievable rate depends on whether the pe rformance criterion is the bit error rate or the message error probabi lity and whether the coding strategy is deterministic or randomized.