Coding for Trace Reconstruction over Multiple Channels with Vanishing Deletion Probabilities

TL;DR

This paper introduces a new coding scheme for trace reconstruction in DNA storage, effective with multiple traces and low deletion probabilities, achieving efficient reconstruction with a constant number of traces.

Contribution

We propose a novel code design enabling efficient trace reconstruction from a constant number of traces in the vanishing deletion probability regime.

Findings

The code achieves successful reconstruction with high probability as sequence length grows.

Simulation results show improved performance over existing methods in terms of edit distance error.

Theoretical analysis confirms the code's effectiveness in the low deletion probability regime.

Abstract

Motivated by DNA-based storage applications, we study the problem of reconstructing a coded sequence from multiple traces. We consider the model where the traces are outputs of independent deletion channels, where each channel deletes each bit of the input codeword \(\mathbf{x} \in \{0,1\}^n\) independently with probability \(p\). We focus on the regime where the deletion probability \(p \to 0\) when \(n\to \infty\). Our main contribution is designing a novel code for trace reconstruction that allows reconstructing a coded sequence efficiently from a constant number of traces. We provide theoretical results on the performance of our code in addition to simulation results where we compare the performance of our code to other reconstruction techniques in terms of the edit distance error.