A Single-Letter 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. In particular, a strong converse is shown to hold 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. We also show that the underlying optimization problem is a convex-concave problem and that an efficient iterative algorithm converges to the optimal solution. In addition, we show that, unlike achievable rates in the literature, the multiletter version of the bound does not improve. A number of examples are discussed throughout the paper.European Research Council under Grant 725411, and by the Spanish Ministry of Economy and Competitiveness under Grant TEC2016-78434-C3-1-R

A Sphere-Packing Error Exponent for Mismatched Decoding

We derive a sphere-packing error exponent for coded transmission over discrete memoryless channels with a fixed decoding metric. By studying the error probability of the code over an auxiliary channel, we find a lower bound to the probability of error of mismatched decoding. The bound is shown to decay exponentially for coding rates smaller than a new upper bound to the mismatch capacity which is established in this paper. For rates higher than the new upper bound, the error probability is shown to be bounded away from zero. The new upper bound is shown to improve over previous upper bounds to the mismatch capacity

A Single-Letter 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. In particular, it is shown that if the rate exceeds the upper-bound, the probability of error tends to one exponentially when the block-length tends to infinity. We also show that the underlying optimization problem is a convex-concave problem and that an efficient iterative algorithm converges to the optimal solution. In addition, we show that, unlike achievable rates in the literature, the multiletter version of the bound cannot not improve. A number of examples are discussed throughout the paper