Two New Families of Asymptotically Optimal Codebooks from Characters of Cyclic Groups

Yang YAN; Yao YAO; Zhi CHEN; Qiuyan WANG

doi:10.1587/transfun.2020EAP1124

Two New Families of Asymptotically Optimal Codebooks from Characters of Cyclic Groups

Yang YAN, Yao YAO, Zhi CHEN, Qiuyan WANG

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Codebooks with small inner-product correlation have applied in direct spread code division multiple access communications, space-time codes and compressed sensing. In general, it is difficult to construct optimal codebooks achieving the Welch bound or the Levenstein bound. This paper focuses on constructing asymptotically optimal codebooks with characters of cyclic groups. Based on the proposed constructions, two classes of asymptotically optimal codebooks with respect to the Welch bound are presented. In addition, parameters of these codebooks are new.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.8 pp.1027-1032

Publication Date: 2021/08/01

Publicized: 2021/02/08

Online ISSN: 1745-1337

DOI: 10.1587/transfun.2020EAP1124

Type of Manuscript: PAPER

Category: Information Theory

Authors

Yang YAN
  Tianjin University of Technology and Education,Putian University, Putian
Yao YAO
  Hubei University of Technology
Zhi CHEN
  Putian University, Putian,Tiangong University
Qiuyan WANG
  Putian University, Putian,Tiangong University

Keyword

code division multiple access, codebooks, asymptotic optimality, Welch bound

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Yang YAN, Yao YAO, Zhi CHEN, Qiuyan WANG, "Two New Families of Asymptotically Optimal Codebooks from Characters of Cyclic Groups" in IEICE TRANSACTIONS on Fundamentals, vol. E104-A, no. 8, pp. 1027-1032, August 2021, doi: 10.1587/transfun.2020EAP1124.
Abstract: Codebooks with small inner-product correlation have applied in direct spread code division multiple access communications, space-time codes and compressed sensing. In general, it is difficult to construct optimal codebooks achieving the Welch bound or the Levenstein bound. This paper focuses on constructing asymptotically optimal codebooks with characters of cyclic groups. Based on the proposed constructions, two classes of asymptotically optimal codebooks with respect to the Welch bound are presented. In addition, parameters of these codebooks are new.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020EAP1124/_p

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@ARTICLE{e104-a_8_1027,
author={Yang YAN, Yao YAO, Zhi CHEN, Qiuyan WANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Two New Families of Asymptotically Optimal Codebooks from Characters of Cyclic Groups},
year={2021},
volume={E104-A},
number={8},
pages={1027-1032},
abstract={Codebooks with small inner-product correlation have applied in direct spread code division multiple access communications, space-time codes and compressed sensing. In general, it is difficult to construct optimal codebooks achieving the Welch bound or the Levenstein bound. This paper focuses on constructing asymptotically optimal codebooks with characters of cyclic groups. Based on the proposed constructions, two classes of asymptotically optimal codebooks with respect to the Welch bound are presented. In addition, parameters of these codebooks are new.},
keywords={},
doi={10.1587/transfun.2020EAP1124},
ISSN={1745-1337},
month={August},}

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TY - JOUR
TI - Two New Families of Asymptotically Optimal Codebooks from Characters of Cyclic Groups
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1027
EP - 1032
AU - Yang YAN
AU - Yao YAO
AU - Zhi CHEN
AU - Qiuyan WANG
PY - 2021
DO - 10.1587/transfun.2020EAP1124
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2021
AB - Codebooks with small inner-product correlation have applied in direct spread code division multiple access communications, space-time codes and compressed sensing. In general, it is difficult to construct optimal codebooks achieving the Welch bound or the Levenstein bound. This paper focuses on constructing asymptotically optimal codebooks with characters of cyclic groups. Based on the proposed constructions, two classes of asymptotically optimal codebooks with respect to the Welch bound are presented. In addition, parameters of these codebooks are new.
ER -