R&D: Concatenated Codes for Recovery From Multiple Reads of DNA Sequences

arXiv has published an article written by Andreas Lenz, Institute for Communications Engineering, Technical University of Munich, DE-80333 Munich, Germany, Issam Maarouf, Simula UiB, N-5006 Bergen, Norway, Lorenz Welter, Antonia Wachter-Zeh, Institute for Communications Engineering, Technical University of Munich, DE-80333 Munich, Germany, Eirik Rosnes, Simula UiB, N-5006 Bergen, Norway, and Alexandre Graell i Amat, Department of Electrical Engineering, Chalmers University of Technology, SE-41296 Gothenburg, Sweden, and Simula UiB, N-5006 Bergen, Norway.

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.“