New Constructions of Codebooks Nearly Meeting the Welch Bound With Equality

An (N, K) codebook C is a set of N unit-norm complex vectors in \BBC K . Optimal codebooks meeting the Welch bound with equality are desirable in a number of areas. However, it is very difficult to construct such optimal codebooks. There have been a number of attempts to construct codebooks nearly m...

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Bibliographic Details
Published in:	IEEE transactions on information theory 2014-02, Vol.60 (2), p.1348-1355
Main Authors:	Hu, Honggang, Wu, Jinsong
Format:	Article
Language:	eng
Subjects:	Amplitudes Applied sciences Asymptotic methods Asymptotic properties BBC Character Codes Coding theory Construction Correlation Correlation analysis difference set Discrete Fourier transforms Educational institutions Exact sciences and technology Finite element analysis Grassmannian line packing Information theory Information, signal and communications theory Mathematical analysis Meetings MWBE codebook Nickel Optimization Telecommunications and information theory Vectors Vectors (mathematics) Welch bound Zinc
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Summary:	An (N, K) codebook C is a set of N unit-norm complex vectors in \BBC K . Optimal codebooks meeting the Welch bound with equality are desirable in a number of areas. However, it is very difficult to construct such optimal codebooks. There have been a number of attempts to construct codebooks nearly meeting the Welch bound with equality, i.e., the maximal cross-correlation amplitude Imax(C) is slightly higher than the Welch bound equality, but asymptotically achieves it for large enough N. In this paper, using difference sets and the product of Abelian groups, we propose new constructions of codebooks nearly meeting the Welch bound with equality. Our methods yield many codebooks with new parameters. In some cases, our constructions are comparable to known constructions.
ISSN:	0018-9448 1557-9654