Codes Correcting Long Duplication Errors

IF 2.4 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC

IEEE Transactions on Molecular, Biological, and Multi-Scale Communications Pub Date : 2024-03-21 DOI:10.1109/TMBMC.2024.3403755

Daniil Goshkoder;Nikita Polyanskii;Ilya Vorobyev

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引用次数: 0

Abstract

We consider the problem of constructing codes capable of correcting long tandem duplication errors of variable length. We present a subquadratic-complexity algorithm that uses only one symbol of redundancy to encode q-ary length-n words into codewords, which can correct a single duplication of length at least

$K=4\cdot \lceil \log _{q} n\rceil +1$

. We enhance the error-correcting capability by introducing codes without efficient encoding, leading to an improved value of

$K= \lceil \log _{q} n\rceil +\phi (n)$

, where

$\phi (n)$

is an arbitrary function such that

$\phi (n)\to \infty $

$n\to \infty $

. In the class of codes correcting a single long duplication with redundancy 1, the value K in our constructions is order-optimal. Finally, k-repeat-free codes, in which every codeword contains any k-tuple at most once, are shown to correct any number of independent long duplications, each of length at least

${K} = 2{k}$

, occurring simultaneously without any mutual interference.

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纠正长重复错误的代码

我们考虑的问题是构建能够纠正长度可变的长串联重复错误的编码。我们提出了一种亚二次复杂度算法，该算法仅使用一个冗余符号将长度为 n 的 qary 字编码成码字，它可以纠正长度至少为 $K=4\cdot \lceil \log _{q} n\rceil +1$ 的单个重复错误。我们通过引入无有效编码的编码来增强纠错能力，从而得到了一个改进的值 $K= \lceil \log _{q} n\rceil +\phi (n)$ ，其中 $\phi (n)$ 是一个任意函数，使得 $\phi (n)\to \infty $ 与 $n\to \infty $ 一样。在纠错冗余度为 1 的单个长重复的编码类别中，我们的构造中的 K 值是阶最优的。最后，K-无重复编码（其中每个编码词最多包含一次 k 元组）被证明可以纠正任意数量的独立长重复，每个重复的长度至少为 ${K} = 2{k}$ ，同时发生而没有任何相互干扰。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.