Concatenated Codes for Recovery From Multiple Reads of DNA Sequences

TL;DR

This paper introduces new decoding algorithms for DNA data storage that improve error correction when multiple sequence reads are available, using concatenated codes and joint probabilistic inference.

Contribution

It proposes two novel decoding algorithms that jointly or separately decode multiple received sequences using a hidden Markov model, enhancing decoding performance.

Findings

Significant performance gains over single sequence decoding

Achievable information rates improved with multiple reads

Monte Carlo simulations validate the algorithms' effectiveness

Abstract

Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a concatenated coding scheme with an outer low-density parity-check code and either an inner convolutional code or a block code. We propose two new decoding algorithms for inference from multiple received sequences, both combining the inner code and channel to a joint hidden Markov model to infer symbolwise a posteriori probabilities (APPs). The first decoder computes the exact APPs by jointly decoding the received sequences, whereas the second decoder approximates the APPs by combining the results of separately decoded received sequences. Using the proposed algorithms, we evaluate the performance of decoding multiple received sequences by means of achievable information rates and Monte-Carlo simulations. We show significant performance gains compared to a single received sequence.