On achievable rates and error exponents for channels with mismatched decoding

The problem of characterizing achievable rates and error exponents for discrete memoryless channels with mismatched decoding is addressed. A mismatched cognitive multiple-access channel is introduced, and an inner bound on its capacity region is derived using two alternative encoding methods: 1) superposition coding and 2) random binning. The inner bounds are derived by analyzing the average error probability of the code ensemble for both methods and by a tight characterization of the resulting error exponents. Random coding converse theorems are also derived. A comparison of the achievable regions shows that in the matched case, random binning performs as well as superposition coding, i.e., the region achievable by random binning is equal to the capacity region. The achievability results are further specialized to obtain a lower bound on the mismatch capacity of the single-user channel by investigating a cognitive multiple-access channel whose achievable sum-rate serves as a lower bound on the single-user channel's capacity. While the achievable rate presented here may not improve the rate achieved by Lapidoth's scheme in optimizing over the parameters of the random coding scheme, it can improve the achieved rate for given parameters, and thereby may reduce the computational complexity required to find a good code.