Construction and redundancy of codes for correcting deletable errors

TL;DR

This paper introduces codes that efficiently correct nearly all deletable error patterns with redundancy growing logarithmically, significantly reducing redundancy compared to traditional methods for correcting all such errors.

Contribution

It presents a novel code construction that corrects nearly all deletable errors with minimal redundancy, improving upon existing codes that correct all errors.

Findings

Redundancy grows logarithmically with code length

Codes correct nearly all deletable error patterns

Significant reduction in redundancy compared to traditional codes

Abstract

Consider a binary word being transmitted through a communication channel that introduces deletable errors where each bit of the word is either retained, flipped, erased or deleted. The simplest code for correcting \emph{all} possible deletable error patterns of a fixed size is the repetition code whose redundancy grows linearly with the code length. In this paper, we relax this condition and construct codes capable of correcting \emph{nearly} all deletable error patterns of a fixed size, with redundancy growing as a logarithm of the word length.