A single-letter upper bound to the mismatch capacity

Kangarshahi, Ehsan Asadi; Guillén i Fábregas, A. (Albert)

doi:http://dx.doi.org/10.1109/TIT.2021.3058070

A single-letter upper bound to the mismatch capacity

Citation

Kangarshahi EA, Guillén i Fàbregas A. A single-letter upper bound to the mismatch capacity. IEEE Trans Inf Theory. 2021;67(4):2013-33. DOI: 10.1109/TIT.2021.3058070

Abstract

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.