# Bit Flipping Moment Balancing Schemes for Insertion, Deletion and Substitution Error Correction

## TL;DR

This paper introduces two efficient bit flipping schemes that modify existing substitution error correcting codes to also correct insertion/deletion errors with minimal additional flips, maintaining code rate and decoder compatibility.

## Contribution

It presents novel moment balancing schemes that enable existing substitution error correcting codes to correct insertion/deletion errors without extra parity bits or decoder modifications.

## Key findings

- The schemes can correct single insertion/deletion errors or multiple substitution errors.
- Number of bit flips remains small relative to code length.
- Applicable to long codes in channels with dominant substitution errors.

## Abstract

In this paper, two moment balancing schemes, namely a variable index scheme and a fixed index scheme, for either single insertion/deletion error correction or multiple substitution error correction are introduced for coded sequences originally developed for correcting substitution errors only. By judiciously flipping bits of the original substitution error correcting code word, the resulting word is able to correct either a reduced number of substitution errors or a single insertion/deletion error. The number of flips introduced by the two schemes can be kept small compared to the code length. It shows a practical value of applying the schemes to a long substitution error correcting code for a severe channel where substitution errors dominate but insertion/deletion errors can occur with a low probability. The new schemes can be more easily implemented in an existing coding system than any previously published moment balancing templates since no additional parity bits are required which also means the code rate remains same and the existing substitution error correcting decoder requires no changes. Moreover, the work extends the class of Levenshtein codes capable of correcting either single substitution or single insertion/deletion errors to codes capable of correcting either multiple substitution errors or single insertion/deletion error.