Pseudo-wigner matrices from dual BCH codes
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Soloveychik, I; Xiang, Y; Tarokh, V
Published in: IEEE International Symposium on Information Theory - Proceedings
August 9, 2017
We consider the problem of generating symmetric pseudo-random sign (±1) matrices based on the similarity of their spectra to Wigner's semicircular law. We introduce r-independent pseudo-Wigner ensembles and prove closeness of their spectra to the semicircular density in Kolmogorov distance. We give an explicit construction of a family of N × N pseudo-Wigner ensembles using dual BCH codes and show that the Kolmogorov complexity of the obtained matrices is of the order of log (N) bits for a fixed Kolmogorov distance precision. Finally, we provide numerical simulations verifying our theoretical results.
Duke Scholars
Published In
IEEE International Symposium on Information Theory - Proceedings
DOI
ISSN
2157-8095
Publication Date
August 9, 2017
Start / End Page
1381 / 1385
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Soloveychik, I., Xiang, Y., & Tarokh, V. (2017). Pseudo-wigner matrices from dual BCH codes. In IEEE International Symposium on Information Theory - Proceedings (pp. 1381–1385). https://doi.org/10.1109/ISIT.2017.8006755
Soloveychik, I., Y. Xiang, and V. Tarokh. “Pseudo-wigner matrices from dual BCH codes.” In IEEE International Symposium on Information Theory - Proceedings, 1381–85, 2017. https://doi.org/10.1109/ISIT.2017.8006755.
Soloveychik I, Xiang Y, Tarokh V. Pseudo-wigner matrices from dual BCH codes. In: IEEE International Symposium on Information Theory - Proceedings. 2017. p. 1381–5.
Soloveychik, I., et al. “Pseudo-wigner matrices from dual BCH codes.” IEEE International Symposium on Information Theory - Proceedings, 2017, pp. 1381–85. Scopus, doi:10.1109/ISIT.2017.8006755.
Soloveychik I, Xiang Y, Tarokh V. Pseudo-wigner matrices from dual BCH codes. IEEE International Symposium on Information Theory - Proceedings. 2017. p. 1381–1385.
Published In
IEEE International Symposium on Information Theory - Proceedings
DOI
ISSN
2157-8095
Publication Date
August 9, 2017
Start / End Page
1381 / 1385