Achievable Information Rates and Concatenated Codes for the DNA Nanopore Sequencing Channel

TL;DR

This paper models the correlated errors in DNA nanopore sequencing as a memory-$k$ channel, derives a MAP decoder to compute achievable information rates, and demonstrates that concatenated codes with LDPC and convolutional codes perform well.

Contribution

It introduces a MAP decoding framework for the memory-$k$ nanopore channel and designs effective concatenated coding schemes for DNA storage.

Findings

Achievable information rates are computed for the DNA nanopore channel.

Concatenated coding schemes significantly improve error correction performance.

MAP decoder enables tailored code design for the DNA storage channel.

Abstract

The errors occurring in DNA-based storage are correlated in nature, which is a direct consequence of the synthesis and sequencing processes. In this paper, we consider the memory-$k$ nanopore channel model recently introduced by Hamoum et al., which models the inherent memory of the channel. We derive the maximum a posteriori (MAP) decoder for this channel model. The derived MAP decoder allows us to compute achievable information rates for the true DNA storage channel assuming a mismatched decoder matched to the memory-$k$ nanopore channel model, and quantify the loss in performance assuming a small memory length--and hence limited decoding complexity. Furthermore, the derived MAP decoder can be used to design error-correcting codes tailored to the DNA storage channel. We show that a concatenated coding scheme with an outer low-density parity-check code and an inner convolutional code yields excellent performance.