Open AccessConstructions of asymptotically optimal codebooks with respect to Welch bound and Levenshtein bound
Author(s) -
Gang Wang,
Dingbang Xu,
Fang-Wei Fu
Publication year - 2023
Publication title -
advances in mathematics of communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.601
H-Index - 26
eISSN - 1930-5346
pISSN - 1930-5338
DOI - 10.3934/amc.2021065
Subject(s) - mathematics , circulant matrix , hadamard transform , asymptotically optimal algorithm , upper and lower bounds , combinatorics , row , code (set theory) , class (philosophy) , discrete mathematics , algorithm , mathematical analysis , artificial intelligence , computer science , set (abstract data type) , database , programming language
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.