Synchronization Strings and Codes for Insertions and Deletions -- a Survey

TL;DR

This survey reviews recent advances in error-correcting codes capable of handling insertions and deletions, highlighting the role of synchronization strings as a key tool for improving robustness against synchronization errors.

Contribution

It provides a comprehensive overview of the development and application of synchronization strings in designing efficient codes for insertion and deletion errors, summarizing recent progress and open problems.

Findings

Synchronization strings enable efficient correction of insertion and deletion errors.

Recent codes can correct a constant fraction of worst-case synchronization errors.

Synchronization strings have broad applications in various communication settings.

Abstract

Already in the 1960s, Levenshtein and others studied error-correcting codes that protect against synchronization errors, such as symbol insertions and deletions. However, despite significant efforts, progress on designing such codes has been lagging until recently, particularly compared to the detailed understanding of error-correcting codes for symbol substitution or erasure errors. This paper surveys the recent progress in designing efficient error-correcting codes over finite alphabets that can correct a constant fraction of worst-case insertions and deletions. Most state-of-the-art results for such codes rely on synchronization strings, simple yet powerful pseudo-random objects that have proven to be very effective solutions for coping with synchronization errors in various settings. This survey also includes an overview of what is known about synchronization strings and discusses communication settings related to error-correcting codes in which synchronization strings have been applied.