Codes Correcting Two Deletions

TL;DR

This paper presents a new coding scheme that corrects two deletions with minimal redundancy, achieving the lowest known number of redundant bits for such codes, advancing the efficiency of error correction in data transmission.

Contribution

The paper introduces the most efficient code for correcting two deletions, requiring approximately 8 log n + O(log log n) bits of redundancy, improving upon previous constructions.

Findings

Redundancy is approximately 8 log n + O(log log n) bits.

This code corrects two deletions with minimal redundancy.

It is the best known construction for this problem.

Abstract

In this work, we investigate the problem of constructing codes capable of correcting two deletions. In particular, we construct a code that requires redundancy approximately 8 log n + O(log log n) bits of redundancy, where n is the length of the code. To the best of the author's knowledge, this represents the best known construction in that it requires the lowest number of redundant bits for a code correcting two deletions.