Matched Metrics and Channels

TL;DR

This paper investigates the relationship between maximum likelihood decoding and nearest neighbor decoding across various channels and metrics, highlighting when these criteria align or differ for general codes.

Contribution

It provides a comprehensive analysis of conditions under which maximum likelihood and nearest neighbor decoding coincide or diverge beyond the Hamming metric.

Findings

Maximum likelihood decoding coincides with nearest neighbor decoding for the binary symmetric channel with Hamming metric.

The paper identifies channels and metrics where the two decoding criteria do not align.

Conditions are characterized for when these decoding methods are equivalent or distinct.

Abstract

The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on the binary symmetric channel. In this work we study channels and metrics for which those two criteria do and do not coincide for general codes.