On Equivalence of Binary Asymmetric Channels regarding the Maximum Likelihood Decoding

TL;DR

This paper characterizes when two binary asymmetric channels are equivalent under maximum likelihood decoding for block codes, providing explicit descriptions of their parameter regions and implications for decoding.

Contribution

It introduces a detailed characterization of channel equivalence classes based on transition probabilities, with explicit formulas and analysis.

Findings

Explicit regions for channel equivalence classes are derived.

The number and size of these regions are quantified.

Implications for decoding strategies are discussed.

Abstract

We study the problem of characterizing when two memoryless binary asymmetric channels, described by their transition probabilities $(p,q)$ and $(p',q')$, are equivalent from the point of view of maximum likelihood decoding (MLD) when restricted to $n$-block binary codes. This equivalence of channels induces a partition (depending on $n$) on the space of parameters $(p,q)$ into regions associated with the equivalence classes. Explicit expressions for describing these regions, their number and areas are derived. Some perspectives of applications of our results to decoding problems are also presented.