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題名 More constructions of near optimal codebooks associated with binary sequences
作者 Chou, Wun-Seng
周文賢
Zhang, Xiyong
Cao, Xiwang
貢獻者 應用數學系
關鍵詞 Codebook; Fourier matrix; Hadamard matrix; Welch bound; character sum
日期 2017-02
上傳時間 2-Aug-2017 16:11:52 (UTC+8)
摘要 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.
關聯 Advances in Mathematics of Communications, 11(1), 187-202
資料類型 article
DOI http://dx.doi.org/10.3934/amc.2017012
dc.contributor 應用數學系zh_Tw
dc.creator (作者) Chou, Wun-Sengen_US
dc.creator (作者) 周文賢zh_TW
dc.creator (作者) Zhang, Xiyongen_US
dc.creator (作者) Cao, Xiwangen_US
dc.date (日期) 2017-02en_US
dc.date.accessioned 2-Aug-2017 16:11:52 (UTC+8)-
dc.date.available 2-Aug-2017 16:11:52 (UTC+8)-
dc.date.issued (上傳時間) 2-Aug-2017 16:11:52 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/111612-
dc.description.abstract (摘要) 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.en_US
dc.format.extent 101 bytes-
dc.format.mimetype text/html-
dc.relation (關聯) Advances in Mathematics of Communications, 11(1), 187-202en_US
dc.subject (關鍵詞) Codebook; Fourier matrix; Hadamard matrix; Welch bound; character sumen_US
dc.title (題名) More constructions of near optimal codebooks associated with binary sequencesen_US
dc.type (資料類型) article-
dc.identifier.doi (DOI) 10.3934/amc.2017012-
dc.doi.uri (DOI) http://dx.doi.org/10.3934/amc.2017012-