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：基于DNA的存储中出现的错误在性质上是相互关联的,这是合成和排序过程的直接结果。在本文中,我们考虑了哈穆姆等人最近推出的内存-一千元纳米波尔信道模型,该模型模拟了频道的固有内存。我们为该频道模型得出了最大后传解码器。衍生的MAP 解码器使我们能够计算出真实DNA存储频道的可实现的信息率,假设一个与内存-一千元纳米波尔频道模型匹配的不匹配的解码器,并用小内存长度和因此有限的解码复杂性来量化性能损失。此外,衍生的MAP 解码器可用于设计适合DNA存储频道的错误校正代码。我们显示,一个与外部低密度对等检查码和内导导码相配的编码方法可以产生极好的性能。