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Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/111612

Title:	More constructions of near optimal codebooks associated with binary sequences
Authors:	Chou, Wun-Seng 周文賢 Zhang, Xiyong Cao, Xiwang
Contributors:	應用數學系
Keywords:	Codebook;Fourier matrix;Hadamard matrix;Welch bound;character sum
Date:	2017-02
Issue Date:	2017-08-02 16:11:52 (UTC+8)
Abstract:	An (N, K) codebook C is a collection of unit norm vectors in a K-dimensional vectors space. In applications of codebooks such as CDMA, those vectors in a codebook should have a small maximum magnitude of inner products, denoted by Imax(C), between any pair of distinct code vectors. Since the famous Welch bound is a lower bound on Imax(C), it is desired to construct codebooks meeting the Welch bound strictly or asymptotically. Recently, N. Y. Yu presents a method for constructing codebooks associated with a binary sequence from a Φ-transform matrix. Using this method, he discovers new classes of codebooks with nontrivial bounds on the maximum inner products from Fourier and Hadamard matrices. We construct more near optimal codebooks by Yu’s idea. We first provide more choices of binary sequences. We also show more choices of the Φ-transform matrices. Therefore, we can present more codebooks C with nontrivial bounds on their Imax(C). Our work can serve as a complement of Yu’s work. © 2017 AIMS.
Relation:	Advances in Mathematics of Communications, 11(1), 187-202
Data Type:	article
DOI 連結:	http://dx.doi.org/10.3934/amc.2017012
DOI:	10.3934/amc.2017012
Appears in Collections:	[應用數學系] 期刊論文

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