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Two constructions of asymptotically optimal codebooks

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Abstract

Codebooks with low-coherence have wide applications in many fields such as direct spread code division multiple access communications, compressed sensing, signal processing and so on. In this paper, we propose two constructions of complex codebooks from the operations of certain sets. The complex codebooks produced by these constructions are proved to be asymptotically optimal with respect to the Welch bound. In addition, the parameters of the complex codebooks presented in this paper are new and flexible in some cases.

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Acknowledgments

We are grateful to the anonymous referees and the editor for useful comments and suggestions that improved the presentation and quality of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Gaojun Luo & Xiwang Cao

  2. State Key Laboratory of Information Security Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Xiwang Cao

Authors
  1. Gaojun Luo
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  2. Xiwang Cao
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Correspondence to Gaojun Luo.

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This work was supported by the National Natural Science Foundations of China (Grant Nos. 11771007 and 61572027)

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Luo, G., Cao, X. Two constructions of asymptotically optimal codebooks. Cryptogr. Commun. 11, 825–838 (2019). https://doi.org/10.1007/s12095-018-0331-4

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  • DOI: https://doi.org/10.1007/s12095-018-0331-4

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