Explicit symmetric pseudo-random matrices

Conference Paper

We consider the problem of generating symmetric pseudo-random sign (±1) matrices based on the similarity of their spectra to Wigner's semicircular law. Using binary m-sequences (Golomb sequences) of lengths n = 2m - 1, we give a simple explicit construction of circulant n × n sign matrices and show that their spectra converge to the semicircular law when n grows. The Kolmogorov complexity of the proposed matrices equals to that of Golomb sequences and is at most 2log2(n) bits.

Full Text

Published version (via Digital Object Identifier)

Duke Authors

Tarokh, Vahid

Cited Authors

Soloveychik, I; Xiang, Y; Tarokh, V

Published Date

January 31, 2018

Published In

Ieee International Symposium on Information Theory Proceedings

Volume / Issue

2018-January /

Start / End Page

424 - 428

International Standard Serial Number (ISSN)

2157-8095

International Standard Book Number 13 (ISBN-13)

9781509030972

Digital Object Identifier (DOI)

10.1109/ITW.2017.8277999

Citation Source

Scopus

Scholars@Duke