# Multilayer Codes for Synchronization from Deletions and Insertions

## TL;DR

This paper introduces a multilayer coding scheme combining VT codes and linear error-correcting codes for efficient one-way synchronization of binary sequences with insertions and deletions, supported by theoretical bounds and simulations.

## Contribution

It proposes a novel multilayer coding approach for synchronization from edits, integrating VT codes with linear codes and analyzing list decoding performance.

## Key findings

- Bounded expected list size under certain assumptions
- Validated performance through numerical simulations
- Trade-off between redundancy and list size in alternative decoding

## Abstract

Consider two remote nodes (encoder and decoder), each with a binary sequence. The encoder's sequence $X$ differs from the decoder's sequence $Y$ by a small number of edits (deletions and insertions). The goal is to construct a message $M$, to be sent via a one-way error free link, such that the decoder can reconstruct $X$ using $M$ and $Y$. In this paper, we devise a coding scheme for this one-way synchronization model. The scheme is based on multiple layers of Varshamov-Tenengolts (VT) codes combined with off-the-shelf linear error-correcting codes, and uses a list decoder. We bound the expected list size of the decoder under certain assumptions, and validate its performance via numerical simulations. We also consider an alternative decoder that uses only the constraints from the VT codes (i.e., does not require a linear code), and has a smaller redundancy at the expense of a slightly larger average list size.