A Family of Codebooks with Nearly Optimal Set Size

Cuiling FAN  Rong LUO  Xiaoni DU  

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
codebook,  signal set,  Levenstein bound,  CDMA,  compressed sensing,  

Full Text: PDF>>
Buy this Article

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.