  The problem of mismatched decoding for discrete memoryless channels 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: superposition coding and 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. In certain
cases, for given auxiliary random variables this bound strictly improves on the
achievable rate derived by Lapidoth.
