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Title: A new weight vector for a tighter Levenshtein bound on aperiodic correlation
Authors: Liu, Zilong
Parampalli, Udaya
Guan, Yong Liang
Boztas, Serdar
Keywords: DRNTU::Engineering::Electrical and electronic engineering
Issue Date: 2013
Source: Liu, Z., Parampalli, U., Guan, Y. L., & Boztas, S. (2014). A New Weight Vector for a Tighter Levenshtein Bound on Aperiodic Correlation. IEEE Transactions on Information Theory, 60(2), 1356-1366.
Series/Report no.: IEEE transactions on information theory
Abstract: The Levenshtein bound on aperiodic correlation, which is a function of the weight vector, is tighter than the Welch bound for sequence sets over the complex roots of unity when M ≥ 4 and n ≥ 2, where M denotes the set size and n the sequence length. Although it is known that the tightest Levenshtein bound is equal to the Welch bound for M ∈ {1,2}, it is unknown whether the Levenshtein bound can be tightened for M=3, and Levenshtein, in his paper published in 1999, postulated that the answer may be negative. A new weight vector is proposed in this paper, which leads to a tighter Levenshtein bound for M=3, n ≥ 3 and M ≥ 4, n ≥ 2. In addition, the explicit form of the weight vector (which is derived by relating the quadratic minimization to the Chebyshev polynomials of the second kind) in Levenshtein's paper is given. Interestingly, this weight vector also yields a tighter Levenshtein bound for M=3, n ≥ 3 and M ≥ 4, n ≥ √M, a fact not noticed by Levenshtein.
ISSN: 0018-9448
DOI: 10.1109/TIT.2013.2293493
Rights: © 2013 IEEE. This is the author created version of a work that has been peer reviewed and accepted for publication by IEEE Transactions on Information Theory, IEEE. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [DOI:].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:EEE Journal Articles

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