A Counter-Example to the Mismatched Decoding Converse for Binary-Input Discrete Memoryless Channels

TL;DR

This paper presents a counter-example in the mismatched decoding problem for binary-input discrete memoryless channels, showing that achievable rates can surpass the LM rate, challenging previous converse results.

Contribution

It provides the first known counter-example where the achievable rate exceeds the LM rate, using both numerical and theoretical methods.

Findings

Achievable rate exceeds the LM rate in the counter-example.

Numerical evaluations support the theoretical findings.

Challenges the previously reported converse result for mismatched decoding.

Abstract

This paper studies the mismatched decoding problem for binary-input discrete memoryless channels. An example is provided for which an achievable rate based on superposition coding exceeds the LM rate (Hui, 1983; Csisz\'ar-K\"orner, 1981), thus providing a counter-example to a previously reported converse result (Balakirsky, 1995). Both numerical evaluations and theoretical results are used in establishing this claim.