A frequency-domain approach to tightening the generalized levenshtein bound

Zilong Liu; Yong Liang Guan; Wai Ho Mow

doi:10.1109/ISIT.2017.8006617

A frequency-domain approach to tightening the generalized levenshtein bound

Zilong Liu, Yong Liang Guan, Wai Ho Mow

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Citations (Scopus)

Abstract

Generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of quasi-complementary sequence set (QCSS) which refers to a set of two-dimensional matrices with low non-trivial aperiodic auto- and cross-correlation sums. GLB is an indefinite fractional quadratic function of a 'simplex' weight vector w and three additional parameters associated with QCSS. We present a novel approach to analytically conduct fractional quadratic optimization for the tightening of the GLB. Our key idea is to apply the frequency-domain decomposition of the relevant circulant matrix (i.e., the numerator term of GLB) to convert the non-convex problem into a convex one. We derive a new weight vector which asymptotically leads to a tighter GLB (over the Welch bound) for all possible (K, M) cases, where K, M denote the set size, the number of channels, of QCSS, respectively.

Original language	English
Title of host publication	2017 IEEE International Symposium on Information Theory, ISIT 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	694-698
Number of pages	5
ISBN (Electronic)	9781509040964
DOIs	https://doi.org/10.1109/ISIT.2017.8006617
Publication status	Published - Aug 9 2017
Externally published	Yes
Event	2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: Jun 25 2017 → Jun 30 2017

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8095

Conference

Conference	2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/Territory	Germany
City	Aachen
Period	6/25/17 → 6/30/17

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

ASJC Scopus Subject Areas

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

Keywords

Fractional quadratic function
Generalized Levenshtein bound (GLB)
Perfect complementary sequence set (PCSS)
Quasi-complementary sequence set (QCSS)
Welch Bound

Access to Document

10.1109/ISIT.2017.8006617

Cite this

Liu, Z., Guan, Y. L., & Mow, W. H. (2017). A frequency-domain approach to tightening the generalized levenshtein bound. In 2017 IEEE International Symposium on Information Theory, ISIT 2017 (pp. 694-698). Article 8006617 (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2017.8006617

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abstract = "Generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of quasi-complementary sequence set (QCSS) which refers to a set of two-dimensional matrices with low non-trivial aperiodic auto- and cross-correlation sums. GLB is an indefinite fractional quadratic function of a 'simplex' weight vector w and three additional parameters associated with QCSS. We present a novel approach to analytically conduct fractional quadratic optimization for the tightening of the GLB. Our key idea is to apply the frequency-domain decomposition of the relevant circulant matrix (i.e., the numerator term of GLB) to convert the non-convex problem into a convex one. We derive a new weight vector which asymptotically leads to a tighter GLB (over the Welch bound) for all possible (K, M) cases, where K, M denote the set size, the number of channels, of QCSS, respectively.",

keywords = "Fractional quadratic function, Generalized Levenshtein bound (GLB), Perfect complementary sequence set (PCSS), Quasi-complementary sequence set (QCSS), Welch Bound",

author = "Zilong Liu and Guan, {Yong Liang} and Mow, {Wai Ho}",

note = "Publisher Copyright: {\textcopyright} 2017 IEEE.; 2017 IEEE International Symposium on Information Theory, ISIT 2017 ; Conference date: 25-06-2017 Through 30-06-2017",

year = "2017",

month = aug,

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doi = "10.1109/ISIT.2017.8006617",

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Liu, Z, Guan, YL & Mow, WH 2017, A frequency-domain approach to tightening the generalized levenshtein bound. in 2017 IEEE International Symposium on Information Theory, ISIT 2017., 8006617, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 694-698, 2017 IEEE International Symposium on Information Theory, ISIT 2017, Aachen, Germany, 6/25/17. https://doi.org/10.1109/ISIT.2017.8006617

A frequency-domain approach to tightening the generalized levenshtein bound. / Liu, Zilong; Guan, Yong Liang; Mow, Wai Ho.
2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 694-698 8006617 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - Generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of quasi-complementary sequence set (QCSS) which refers to a set of two-dimensional matrices with low non-trivial aperiodic auto- and cross-correlation sums. GLB is an indefinite fractional quadratic function of a 'simplex' weight vector w and three additional parameters associated with QCSS. We present a novel approach to analytically conduct fractional quadratic optimization for the tightening of the GLB. Our key idea is to apply the frequency-domain decomposition of the relevant circulant matrix (i.e., the numerator term of GLB) to convert the non-convex problem into a convex one. We derive a new weight vector which asymptotically leads to a tighter GLB (over the Welch bound) for all possible (K, M) cases, where K, M denote the set size, the number of channels, of QCSS, respectively.

AB - Generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of quasi-complementary sequence set (QCSS) which refers to a set of two-dimensional matrices with low non-trivial aperiodic auto- and cross-correlation sums. GLB is an indefinite fractional quadratic function of a 'simplex' weight vector w and three additional parameters associated with QCSS. We present a novel approach to analytically conduct fractional quadratic optimization for the tightening of the GLB. Our key idea is to apply the frequency-domain decomposition of the relevant circulant matrix (i.e., the numerator term of GLB) to convert the non-convex problem into a convex one. We derive a new weight vector which asymptotically leads to a tighter GLB (over the Welch bound) for all possible (K, M) cases, where K, M denote the set size, the number of channels, of QCSS, respectively.

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A frequency-domain approach to tightening the generalized levenshtein bound

Abstract

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Bibliographical note

ASJC Scopus Subject Areas

Keywords

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