An Upper Bound to the Mismatch Capacity

We derive a single-letter upper bound to the mismatched-decoding capacity for discrete memoryless channels. The bound is expressed as the mutual information of a transformation of the channel, such that a maximum-likelihood decoding error on the translated channel implies a mismatched-decoding error in the original channel. We show this bound recovers the binary-input binary-output mismatch capacity which is known to either be the channel capacity or zero. In addition, a strong converse is shown for this upper bound: if the rate exceeds the upper-bound, the probability of error tends to 1 exponentially when the block-length tends to infinity.