A class of nearly optimal codebooks and their applications in strongly regular Cayley graphs-Reference-Cited by-同舟云学术

A class of nearly optimal codebooks and their applications in strongly regular Cayley graphs

Published:2024 Issue:7 Volume:9 Page:18236-18246
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Wang Qiuyan¹²,Liu Weixin¹,Wang Jianming¹²,Yan Yang³

Affiliation:

1. School of Computer Science and Technology, Tiangong University, Tianjin 300387 China

2. Tianjin Key Laboratory of Autonomous Intelligence Technology and Systems, Tiangong University, Tianjin 300387, China

3. School of Information Technology and Engineering, Tianjin University of Technology and Education, Tianjin 300222 China

Abstract

<abstract><p>Codebooks with small inner-product correlations are desirable in many fields, including compressed sensing, direct spread code division multiple access (CDMA) systems, and space-time codes. The objective of this paper is to present a class of codebooks and explore their applications in strongly regular Cayley graphs. The obtained codebooks are nearly optimal in the sense that their maximum cross-correlation amplitude nearly meets the Welch bound. As far as we know, this construction of codebooks provides new parameters.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference25 articles.

1. L. Welch, Lower bounds on the maximum cross correlation of signals, IEEE T. Inform. Theory, 20 (1974), 397–399. https://doi.org/10.1109/TIT.1974.1055219

2. J. H. Conway, R. H. Harding, N. J. A. Sloane, Packing lines, planes, etc.: Packings in Grassmannian spaces, Exp. Math., 5 (1996), 139–159. https://doi.org/10.1080/10586458.1996.10504585

3. C. Ding, Complex codebooks from combinatorial designs, IEEE T. Inform. Theory, 52 (2006), 4229–4235. https://doi.org/10.1109/TIT.2006.880058

4. M. Fickus, D. G. Mixon, J. Jasper, Equiangular tight frames from hyperovals, IEEE T. Inform. Theory, 62 (2016), 5225–5236. https://doi.org/10.1109/TIT.2016.2587865

5. M. Fickus, D. G. Mixon, J. C. Tremain, Steiner equiangular tight frames, Linear Algebra Appl., 436 (2012), 1014–1027. https://doi.org/10.1016/j.laa.2011.06.027