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| Title | More constructions of near optimal codebooks associated with binary sequences |
| Creator | Chou, Wun-Seng 周文賢 Zhang, Xiyong Cao, Xiwang |
| Contributor | 應用數學系 |
| Key Words | Codebook; Fourier matrix; Hadamard matrix; Welch bound; character sum |
| Date | 2017-02 |
| Date Issued | 2-Aug-2017 16:11:52 (UTC+8) |
| Summary | 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 |
| Type | 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-Seng | en_US |
| dc.creator (作者) | 周文賢 | zh_TW |
| dc.creator (作者) | Zhang, Xiyong | en_US |
| dc.creator (作者) | Cao, Xiwang | en_US |
| dc.date (日期) | 2017-02 | en_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), 187-202 | en_US |
| dc.subject (關鍵詞) | Codebook; Fourier matrix; Hadamard matrix; Welch bound; character sum | en_US |
| dc.title (題名) | More constructions of near optimal codebooks associated with binary sequences | en_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 | - |