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.

翻译：DNA存储中出现的错误本质上具有相关性，这是合成与测序过程的直接结果。本文考虑Hamoum等人近期提出的记忆$k$纳米孔信道模型，该模型刻画了信道固有的记忆特性。我们推导了该信道模型的最大后验概率（MAP）译码器。通过所推导的MAP译码器，我们能够计算真实DNA存储信道在采用匹配记忆$k$纳米孔信道模型的失配译码器时的可达信息率，并量化采用短记忆长度（因而译码复杂度受限）时的性能损失。此外，所推导的MAP译码器可用于设计面向DNA存储信道的纠错码。我们证明，采用外低密度奇偶校验码与内卷积码的级联编码方案能够获得优异的性能表现。