吲哚码和替换校正码的最大心数界限

IF 2.4 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC

IEEE Transactions on Molecular, Biological, and Multi-Scale Communications Pub Date : 2024-04-16 DOI:10.1109/TMBMC.2024.3388971

Ward J. P. Spee;Jos H. Weber

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引用次数: 0

摘要

DNA 数据存储领域的最新进展再次吸引了人们对删除、插入和置换纠错码的关注。与旨在纠正置换错误或删除和插入（indel）错误的代码相比，人们对纠正置换和indel错误组合的代码的理解相对滞后。在本文中，我们重点研究了 qary t-indel s-substitution 纠错码的最大大小。我们的主要贡献包括两个受 Gilbert-Varshamov 启发的关于该大小的下界。在上界方面，我们证明了一个类似 Singleton- 的上界、一系列球形堆积上界和一个整数线性规划上界。我们证明了其中几个边界对现有结果的改进。此外，我们还利用这些边界推导出了最大尺寸 t-indel s 置换校正码渐近冗余度的下界和上界。

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Bounds on the Maximum Cardinality of Indel and Substitution Correcting Codes

Recent advances in DNA data storage have attracted renewed attention towards deletion, insertion and substitution correcting codes. Compared to codes aimed at correcting either substitution errors or deletion and insertion (indel) errors, the understanding of codes that correct combinations of substitution and indel errors lags behind. In this paper, we focus on the maximal size of q-ary t-indel s-substitution correcting codes.Our main contributions include two Gilbert-Varshamov inspired lower bounds on this size. On the upper bound side, we prove a Singleton-like bound, a family of sphere-packing upper bounds and an integer linear programming bound. Several of these bounds are shown to improve upon existing results. Moreover, we use these bounds to derive a lower bound and an upper bound on the asymptotic redundancy of maximally sized t-indel s-substitution correcting codes.

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来源期刊

IEEE Transactions on Molecular, Biological, and Multi-Scale Communications Mathematics-Modeling and Simulation

CiteScore

3.90

自引率

13.60%

发文量

期刊介绍： As a result of recent advances in MEMS/NEMS and systems biology, as well as the emergence of synthetic bacteria and lab/process-on-a-chip techniques, it is now possible to design chemical “circuits”, custom organisms, micro/nanoscale swarms of devices, and a host of other new systems. This success opens up a new frontier for interdisciplinary communications techniques using chemistry, biology, and other principles that have not been considered in the communications literature. The IEEE Transactions on Molecular, Biological, and Multi-Scale Communications (T-MBMSC) is devoted to the principles, design, and analysis of communication systems that use physics beyond classical electromagnetism. This includes molecular, quantum, and other physical, chemical and biological techniques; as well as new communication techniques at small scales or across multiple scales (e.g., nano to micro to macro; note that strictly nanoscale systems, 1-100 nm, are outside the scope of this journal). Original research articles on one or more of the following topics are within scope: mathematical modeling, information/communication and network theoretic analysis, standardization and industrial applications, and analytical or experimental studies on communication processes or networks in biology. Contributions on related topics may also be considered for publication. Contributions from researchers outside the IEEE’s typical audience are encouraged.