Constructions of Complex Codebooks Asymptotically Meeting the Welch Bound: A Graph Theoretic Approach

Shohei Satake; Yujie Gu

doi:10.1109/ISIT44484.2020.9174496

Constructions of Complex Codebooks Asymptotically Meeting the Welch Bound: A Graph Theoretic Approach

Shohei Satake, Yujie Gu

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

Complex codebooks with small inner-product correlation have many applications such as in code-division multiple access communications and compressed sensing. It is desirable but difficult to construct optimal codebooks achieving the well-known Welch bound. In this paper, complex codebooks are investigated from a graph theoretic perspective. A connection between codebooks and Cayley sum graphs is established. Based on this, many infinite families of complex codebooks are explicitly constructed, which are asymptotically optimal with respect to the Welch bound. These constructions not only include some known constructions as special cases but also provide flexible new parameters.

Original language	English
Title of host publication	2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	48-53
Number of pages	6
ISBN (Electronic)	9781728164328
DOIs	https://doi.org/10.1109/ISIT44484.2020.9174496
Publication status	Published - Jun 2020
Externally published	Yes
Event	2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States Duration: Jul 21 2020 → Jul 26 2020

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2020-June
ISSN (Print)	2157-8095

Conference

Conference	2020 IEEE International Symposium on Information Theory, ISIT 2020
Country/Territory	United States
City	Los Angeles
Period	7/21/20 → 7/26/20

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

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10.1109/ISIT44484.2020.9174496

Cite this

Satake, S., & Gu, Y. (2020). Constructions of Complex Codebooks Asymptotically Meeting the Welch Bound: A Graph Theoretic Approach. In 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings (pp. 48-53). [9174496] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT44484.2020.9174496

Constructions of Complex Codebooks Asymptotically Meeting the Welch Bound: A Graph Theoretic Approach. / Satake, Shohei; Gu, Yujie.
2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2020. p. 48-53 9174496 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Satake, S & Gu, Y 2020, Constructions of Complex Codebooks Asymptotically Meeting the Welch Bound: A Graph Theoretic Approach. in 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings., 9174496, IEEE International Symposium on Information Theory - Proceedings, vol. 2020-June, Institute of Electrical and Electronics Engineers Inc., pp. 48-53, 2020 IEEE International Symposium on Information Theory, ISIT 2020, Los Angeles, United States, 7/21/20. https://doi.org/10.1109/ISIT44484.2020.9174496

Satake S, Gu Y. Constructions of Complex Codebooks Asymptotically Meeting the Welch Bound: A Graph Theoretic Approach. In 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2020. p. 48-53. 9174496. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT44484.2020.9174496

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AB - Complex codebooks with small inner-product correlation have many applications such as in code-division multiple access communications and compressed sensing. It is desirable but difficult to construct optimal codebooks achieving the well-known Welch bound. In this paper, complex codebooks are investigated from a graph theoretic perspective. A connection between codebooks and Cayley sum graphs is established. Based on this, many infinite families of complex codebooks are explicitly constructed, which are asymptotically optimal with respect to the Welch bound. These constructions not only include some known constructions as special cases but also provide flexible new parameters.

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Constructions of Complex Codebooks Asymptotically Meeting the Welch Bound: A Graph Theoretic Approach

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