Noisy shuffling channels capture the main characteristics of DNA storage systems where distinct segments of data are received out of order, after being corrupted by substitution errors. For realistic schemes with short-length segments, practical indexing and channel coding strategies are required to restore the order and combat the channel noise. In this paper, we develop a finite-length concatenated coding scheme that employs Reed-Solomon (RS) codes as outer codes and polar codes as inner codes, and utilizes an implicit indexing method based on cosets of the polar code. We propose a matched decoding method along with a metric for detecting the index that successfully restores the order, and correct channel errors at the receiver. Residual errors that are not corrected by the matched decoder are then corrected by the outer RS code. We derive analytical approximations for the frame error rate of the proposed scheme, and also evaluate its performance through simulations to demonstrate that the proposed implicit indexing method outperforms explicit indexing.

翻译：噪声混洗信道捕捉了DNA存储系统的主要特征，其中数据的独立片段在经历替换错误后以乱序方式接收。对于具有短长度片段的实际方案，需要实用的索引和信道编码策略来恢复顺序并抵抗信道噪声。本文提出了一种有限长度级联编码方案，该方案采用里德-所罗门码作为外码、极化码作为内码，并利用基于极化码陪集的隐式索引方法。我们提出了一种匹配解码方法及相应的索引检测度量，该方法能成功恢复数据顺序并在接收端纠正信道错误。匹配解码器未能纠正的残留错误则由外层的里德-所罗门码进行纠正。我们推导了所提方案帧错误率的解析近似表达式，并通过仿真评估其性能，结果表明所提出的隐式索引方法优于显式索引方案。