We propose a list-decoding scheme for reconstruction codes in the context of uniform-tandem-duplication noise, which can be viewed as an application of the associative memory model to this setting. We find the uncertainty associated with $m>2$ strings (where a previous paper considered $m=2$) in asymptotic terms, where code-words are taken from an error-correcting code. Thus, we find the trade-off between the design minimum distance, the number of errors, the acceptable list size and the resulting uncertainty, which corresponds to the required number of distinct retrieved outputs for successful reconstruction. It is therefore seen that by accepting list-decoding one may decrease coding redundancy, or the required number of reads, or both.

中文翻译：

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来自均匀串联重复噪声的列表解码重构的不确定性

我们提出了一种在均匀串联重复噪声背景下重建代码的列表解码方案，可以将其视为关联内存模型在此设置中的应用。我们发现与 $m>2$ 字符串相关的不确定性（之前的论文认为 $m=2$）在渐近项中，其中代码字取自纠错代码。因此，我们找到了设计最小距离、错误数量、可接受的列表大小和由此产生的不确定性之间的权衡，这对应于成功重建所需的不同检索输出的数量。因此可以看出，通过接受列表解码，可以减少编码冗余或所需的读取次数，或两者兼而有之。