Concatenated Codes for Multiple Reads of a DNA Sequence
Journal article, 2023

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.

concatenated codes

DNA storage

polar code

low-density parity-check (LDPC) code

Achievable information rates

synchronization codes

insertion/deletion/substitution (IDS) channel


Issam Maarouf

Simula UiB

Andreas Lenz

Technical University of Munich

Lorenz Welter

Technical University of Munich

Antonia Wachter-Zeh

Technical University of Munich

Eirik Rosnes

Simula UiB

Alexandre Graell I Amat

Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks

Simula UiB

IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 69 2 910-927

Reliable and Secure Coded Edge Computing

Swedish Research Council (VR) (2020-03687), 2021-01-01 -- 2024-12-31.

Subject Categories


Communication Systems

Signal Processing



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