Achievable and Converse bounds over a general channel and general decoding metric

TL;DR

This paper derives tight achievable and converse bounds for general channels with mismatched decoding, providing insights into the optimal performance limits of coding schemes under various decoding metrics.

Contribution

It introduces a unified framework for bounds over general channels and decoding metrics, including a tight analysis and a connection to the minimax meta-converse.

Findings

Achievable bounds are tight up to a factor of 2.

Converse bounds are expressed in terms of the achievable bounds.

In the matched case, the converse matches the minimax meta-converse.

Abstract

Achievable and converse bounds for general channels and mismatched decoding are derived. The direct (achievable) bound is derived using random coding and the analysis is tight up to factor 2. The converse is given in term of the achievable bound and the factor between them is given. This gives performance of the best rate-R code with possible mismatched decoding metric over a general channel, up to the factor that is identified. In the matched case we show that the converse equals the minimax meta-converse of Polyanskiy et al.