Scholars@Duke

Symmetric Pseudo-Random Matrices

Publication ,  Journal Article
Soloveychik, I; Xiang, Y; Tarokh, V
Published in: IEEE Transactions on Information Theory
April 1, 2018
Published version (DOI)

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.

Duke Scholars

Vahid Tarokh
Author Vahid Tarokh Electrical and Computer Engineering

Published In

IEEE Transactions on Information Theory

DOI

10.1109/TIT.2018.2800004

ISSN

0018-9448

Publication Date

April 1, 2018

Volume

64

Issue

4

Start / End Page

3179 / 3196

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing
 

Citation

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ICMJE
MLA
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Soloveychik, I., Xiang, Y., & Tarokh, V. (2018). Symmetric Pseudo-Random Matrices. IEEE Transactions on Information Theory, 64(4), 3179–3196. https://doi.org/10.1109/TIT.2018.2800004
Soloveychik, I., Y. Xiang, and V. Tarokh. “Symmetric Pseudo-Random Matrices.” IEEE Transactions on Information Theory 64, no. 4 (April 1, 2018): 3179–96. https://doi.org/10.1109/TIT.2018.2800004.
Soloveychik I, Xiang Y, Tarokh V. Symmetric Pseudo-Random Matrices. IEEE Transactions on Information Theory. 2018 Apr 1;64(4):3179–96.
Soloveychik, I., et al. “Symmetric Pseudo-Random Matrices.” IEEE Transactions on Information Theory, vol. 64, no. 4, Apr. 2018, pp. 3179–96. Scopus, doi:10.1109/TIT.2018.2800004.
Soloveychik I, Xiang Y, Tarokh V. Symmetric Pseudo-Random Matrices. IEEE Transactions on Information Theory. 2018 Apr 1;64(4):3179–3196.

Published In

IEEE Transactions on Information Theory

DOI

10.1109/TIT.2018.2800004

ISSN

0018-9448

Publication Date

April 1, 2018

Volume

64

Issue

4

Start / End Page

3179 / 3196

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing