A Family of Codebooks with Nearly Optimal Set Size

Cuiling FAN  Rong LUO  Xiaoni DU  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.5   pp.994-997
Publication Date: 2016/05/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.994
Type of Manuscript: LETTER
Category: Coding Theory
Keyword: 
codebook,  signal set,  Levenstein bound,  CDMA,  compressed sensing,  

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Summary: 
Codebooks with good parameters are preferred in many practical applications, such as direct spread CDMA communications and compressed sensing. In this letter, an upper bound on the set size of a codebook is introduced by modifying the Levenstein bound on the maximum amplitudes of such a codebook. Based on an estimate of a class of character sums over a finite field by Katz, a family of codebooks nearly meeting the modified bound is proposed.