Concatenated Codes for Multiple Reads of a DNA Sequence

TL;DR

This paper introduces novel decoding algorithms for concatenated DNA storage codes that efficiently decode multiple received sequences, significantly improving error correction performance over single-sequence decoding.

Contribution

It proposes two joint decoding algorithms based on hidden Markov models for multiple DNA sequence reads, enhancing decoding accuracy and efficiency.

Findings

Significant performance gains over single-sequence decoding.

Joint decoding algorithms improve achievable information rates.

Optimizing inner and outer codes further enhances performance.

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 nonbinary low-density parity-check code or a polar code and either an inner convolutional code or a time-varying block code. We propose two novel 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 and has a complexity that is linear with the number of 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. In addition, we succeed in improving the performance of the aforementioned coding scheme by optimizing both the inner and outer codes.