论文标题
编码索引DNA存储的错误概率范围
Error Probability Bounds for Coded-Index DNA Storage
论文作者
论文摘要
考虑到DNA存储通道，其中代码字由$ M $无序的DNA分子组成。在阅读时，对$ n $分子进行了替换，然后对每个分子进行测序。考虑了一个编码索引串联编码方案，其中代码字的$ M $ TH分子仅限于所有可能的分子的子集（一个内部代码），这对于每个$ M $都是唯一的。解码器具有低复杂性，并且基于第一次分别解码每个分子（内部代码），然后解码分子的序列（外代码）。仅存在内部代码和解码器的形式，仅在测序通道上做出温和的假设。分析了随机代码以及消除代码的错误概率，并以$ n $呈指数衰减。这确立了增加覆盖范围深度$ n/m $的重要性，以获得低误差概率。
The DNA storage channel is considered, in which a codeword is comprised of $M$ unordered DNA molecules. At reading time, $N$ molecules are sampled with replacement, and then each molecule is sequenced. A coded-index concatenated-coding scheme is considered, in which the $m$th molecule of the codeword is restricted to a subset of all possible molecules (an inner code), which is unique for each $m$. The decoder has low-complexity, and is based on first decoding each molecule separately (the inner code), and then decoding the sequence of molecules (an outer code). Only mild assumptions are made on the sequencing channel, in the form of the existence of an inner code and decoder with vanishing error. The error probability of a random code as well as an expurgated code is analyzed and shown to decay exponentially with $N$. This establishes the importance of increasing the coverage depth $N/M$ in order to obtain low error probability.
