Constructions of asymptotically optimal codebooks with respect to Welch bound and Levenshtein bound

IF 0.7 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI:10.3934/amc.2021065

Gang Wang, Deng-Ming Xu, Fang-Wei Fu

引用次数: 0

Abstract

Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in code division multiple access communication systems. In this paper, several classes of codebooks are introduced, whose maximum cross-correlation amplitudes asymptotically achieve the corresponding Welch bound and Levenshtein bound. Specially, a class of optimal codebooks with respect to the Levenshtein bound is obtained. These classes of codebooks are constructed by selecting certain rows deterministically from circulant matrices, Fourier matrices and Hadamard matrices, respectively. The construction methods and parameters of some codebooks provided in this paper are new.

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关于Welch界和Levenshtein界的渐近最优码本构造

在码分多址通信系统中，利用最大互相关幅度较小的码本来区分来自不同用户的信号。本文介绍了几类码本，它们的最大互相关幅度渐近地达到相应的Welch界和Levenshtein界。特别地，得到了一类关于Levenshtein界的最优码本。这类码本分别通过从循环矩阵、傅里叶矩阵和Hadamard矩阵中确定性地选择某些行来构造。文中提供的一些码本的构造方法和参数是新的。

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

Advances in Mathematics of Communications 工程技术-计算机：理论方法

CiteScore

2.20

自引率

22.20%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Mathematics of Communications (AMC) publishes original research papers of the highest quality in all areas of mathematics and computer science which are relevant to applications in communications technology. For this reason, submissions from many areas of mathematics are invited, provided these show a high level of originality, new techniques, an innovative approach, novel methodologies, or otherwise a high level of depth and sophistication. Any work that does not conform to these standards will be rejected. Areas covered include coding theory, cryptology, combinatorics, finite geometry, algebra and number theory, but are not restricted to these. This journal also aims to cover the algorithmic and computational aspects of these disciplines. Hence, all mathematics and computer science contributions of appropriate depth and relevance to the above mentioned applications in communications technology are welcome. More detailed indication of the journal''s scope is given by the subject interests of the members of the board of editors.