A Sphere-Packing Error Exponent for Mismatched Decoding

TL;DR

This paper establishes a new sphere-packing error exponent for mismatched decoding over discrete memoryless channels, providing tighter bounds on error probability and mismatch capacity, advancing understanding of decoding performance.

Contribution

It introduces a novel upper bound to the mismatch capacity and derives a sphere-packing error exponent for mismatched decoding, improving upon previous bounds.

Findings

Error probability decays exponentially below the new capacity bound

Error probability is bounded away from zero above the capacity bound

The new upper bound improves previous mismatch capacity bounds

Abstract

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.