A Refinement of Expurgation

TL;DR

This paper demonstrates that for various channels and code ensembles, removing a tiny fraction of codewords from a random code can achieve the improved expurgated error exponent with high probability as code length increases.

Contribution

It shows that minimal codeword removal from random codes reliably achieves the expurgated exponent across many channels and code ensembles.

Findings

Expurgation leads to improved error exponents.

High probability of success as code length grows.

Applicable to a wide range of channels and code ensembles.

Abstract

We show that for a wide range of channels and code ensembles with pairwise-independent codewords, with probability tending to 1 with the code length, expurgating an arbitrarily small fraction of codewords from a randomly selected code results in a code attaining the expurgated exponent.