Efficiently decodable insertion/deletion codes for high-noise and high-rate regimes

TL;DR

This paper develops efficient decoding algorithms for insertion/deletion codes that operate effectively in high-noise, high-rate regimes across various alphabet sizes, extending previous deletion-only results.

Contribution

It introduces the first constructions of efficiently decodable insertion/deletion codes in high-noise, high-rate regimes for multiple parameter settings, complementing prior deletion-only work.

Findings

Codes achieve near-capacity error correction in high-noise regimes

Efficient decoding algorithms are provided for all constructed codes

The results extend the understanding of insertion/deletion error correction capabilities

Abstract

This work constructs codes that are efficiently decodable from a constant fraction of \emph{worst-case} insertion and deletion errors in three parameter settings: (i) Binary codes with rate approaching 1; (ii) Codes with constant rate for error fraction approaching 1 over fixed alphabet size; and (iii) Constant rate codes over an alphabet of size $k$ for error fraction approaching $(k-1)/(k+1)$. When errors are constrained to deletions alone, efficiently decodable codes in each of these regimes were constructed recently. We complete the picture by constructing similar codes that are efficiently decodable in the insertion/deletion regime.