# Coding for Deletion Channels with Multiple Traces

## TL;DR

This paper introduces low-complexity coding schemes for deletion channels using multiple traces, inspired by DNA storage, enabling efficient reconstruction with linear encoding and decoding complexities.

## Contribution

It proposes simple, explicit codes based on VT codes that leverage multiple traces to improve deletion correction in DNA storage applications.

## Key findings

- Codes are based on VT codes split into blocks.
- Multiple traces help identify deletion-free blocks.
- Encoding is linear; decoding is linear in length, quadratic in deletions and traces.

## Abstract

Motivated by the sequence reconstruction problem from traces in DNA-based storage, we consider the problem of designing codes for the deletion channel when multiple observations (or traces) are available to the decoder. We propose simple binary and non-binary codes based on Varshamov-Tenengolts (VT) codes. The proposed codes split the codeword in blocks and employ a VT code in each block. The availability of multiple traces helps the decoder to identify deletion-free copies of a block, and to avoid mis-synchronization while decoding. The encoding complexity of the proposed scheme is linear in the codeword length; the decoding complexity is linear in the codeword length, and quadratic in the number of deletions and the number of traces. The proposed scheme offers an explicit low-complexity technique for correcting deletions using multiple traces.