修正纳米孔测序读取中的多重替换错误
Correcting Multiple Substitutions in Nanopore-Sequencing Reads
AI总结：
针对纳米孔测序高错误率问题，采用简化模型，利用团覆盖技术证明纠正多个替换错误至少需t log n冗余，并给出常数最优的纠错码。
摘要：
尽管纳米孔测序仪相较于竞争技术具有显著优势，但其高错误率问题依然突出，这源于纳米孔的物理特性以及生物过程中固有的噪声。因此，不仅需要为这些信道设计高效的纠错构造，还需建立此类编码方案所需最小冗余度的界限。在此背景下，我们借鉴Mao等人的工作，采用一种简化的纳米孔测序模型，该模型考虑了符号间干扰和测量噪声的影响。对于长度为$n$的输入序列，所产生的向量（称为读取向量）可能额外遭受至多$t$个替换错误。我们利用著名的图论团覆盖技术，证明要纠正多个（$t \geq 2$）替换错误，至少需要$t\log n -O(1)$比特的冗余度。虽然与单个替换错误的情况（仅需至多$\log \log n - O(1)$比特冗余度）相比，这一结果令人惊讶，但根据读取向量的性质，可以立即得到一个在常数因子内最优的合适纠错码。
英文摘要：
Despite their significant advantages over competing technologies, nanopore sequencers are plagued by high error rates, due to physical characteristics of the nanopore and inherent noise in the biological processes. It is thus paramount not only to formulate efficient error-correcting constructions for these channels, but also to establish bounds on the minimum redundancy required by such coding schemes. In this context, we adopt a simplified model of nanopore sequencing inspired by the work of Mao \emph{et al.}, accounting for the effects of intersymbol interference and measurement noise. For an input sequence of length $n$, the vector that is produced, designated as the \emph{read vector}, may additionally suffer at most \(t\) substitution errors. We employ the well-known graph-theoretic clique-cover technique to establish that at least \(t\log n -O(1)\) bits of redundancy are required to correct multiple (\(t \geq 2\)) substitutions. While this is surprising in comparison to the case of a single substitution, that necessitates at most \(\log \log n - O(1)\) bits of redundancy, a suitable error-correcting code that is optimal up to a constant follows immediately from the properties of read vectors.
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