Matched Metrics to the Binary Asymmetric Channels

TL;DR

This paper proves that every binary asymmetric channel admits a matched metric, providing criteria for when maximum likelihood decoding aligns with nearest neighbor decoding in discrete memoryless channels.

Contribution

It establishes criteria for matched metrics in channels and confirms a conjecture that all binary asymmetric channels admit such metrics.

Findings

Every binary asymmetric channel admits a matched metric.

Provides criteria for the existence of matched metrics in discrete channels.

Confirms a conjecture by Firer and Walker.

Abstract

In this paper we establish some criteria to decide when a discrete memoryless channel admits a metric in such a way that the maximum likelihood decoding coincides with the nearest neighbour decoding. In particular we prove a conjecture presented by M. Firer and J. L. Walker establishing that every binary asymmetric channel admits a matched metric.