Mismatched decoding reliability function at zero rate

TL;DR

This paper derives an upper bound on the reliability function for zero-rate mismatched decoding, showing it matches the expurgated exponent for many channel-decoding metric pairs, advancing understanding of decoding performance limits.

Contribution

It introduces a new upper bound on the reliability function at zero rate for mismatched decoding, utilizing symmetry properties of subcodes, and aligns with the expurgated exponent in broad cases.

Findings

The upper bound coincides with the expurgated exponent at zero rate.

The bound applies to a broad family of channel-decoding metric pairs.

Utilizes a symmetry-based approach inspired by Komlós' result.

Abstract

We derive an upper bound on the reliability function of mismatched decoding for zero-rate codes. The bound is based on a result by Koml\'os that shows the existence of a subcode with certain symmetry properties. The bound is shown to coincide with the expurgated exponent at rate zero for a broad family of channel-decoding metric pairs.