Asymptotically Optimal Codes Correcting One Substring Edit

TL;DR

This paper introduces a coding scheme that corrects a single substring edit with redundancy close to the theoretical minimum, improving error correction efficiency for localized string modifications.

Contribution

The paper presents an asymptotically optimal code construction for correcting one substring edit with minimal redundancy, advancing error correction capabilities.

Findings

Redundancy of the constructed codes is log n + O(log log n), matching the lower bound.

The code corrects localized substring edits including insertions, deletions, and substitutions.

Achieves near-optimal redundancy for correcting one substring edit.

Abstract

The substring edit error is the operation of replacing a substring $u$ of $x$ with another string $v$, where the lengths of $u$ and $v$ are bounded by a given constant $k$. It encompasses localized insertions, deletions, and substitutions within a window. Codes correcting one substring edit have redundancy at least $\log n+k$. In this paper, we construct codes correcting one substring edit with redundancy $\log n+O(\log \log n)$, which is asymptotically optimal.