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2011•Unpublished venueOpen access

Improved lower bound for quasi-complementary sequence set

Zilong Liu, Yong Liang Guan, Wai Ho Mow

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Abstract

The Welch bound for aperiodic correlation for binary sequence set was improved by Levenshtein by weighting the cyclic shifts of the sequence vectors. Taking Levenshtein's idea, a new lower bound for quasi-complementary sequence set (QCSS) over the complex roots-of-unity is derived in this paper. It is shown to be tighter than the Welch bound for QCSS in one of the following cases: 1) K = 4M − 1, M ≥ 2 and equation; 2) K ≥ 4M, M ≥ 2 and N ≥ 2. where K,M,N respectively denotes the set size, number of channels, elementary sequence length of QCSS.

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What this paper is about

The Welch bound for aperiodic correlation for binary sequence set was improved by Levenshtein by weighting the cyclic shifts of the sequence vectors. Taking Levenshtein's idea, a new lower bound for quasi-complementary sequence set (QCSS) over the complex roots-of-unity is derived in this paper. It is shown to be tighter than the Welch bound for QCSS in one of the following cases: 1) K = 4M − 1, M ≥ 2 and equation; 2) K ≥ 4M, M ≥ 2 and N ≥ 2. where K,M,N respectively denotes the set size, number of channels, elementary sequence length of QCSS.

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Available abstract

The Welch bound for aperiodic correlation for binary sequence set was improved by Levenshtein by weighting the cyclic shifts of the sequence vectors. Taking Levenshtein's idea, a new lower bound for quasi-complementary sequence set (QCSS) over the complex roots-of-unity is derived in this paper. It is shown to be tighter than the Welch bound for QCSS in one of the following cases: 1) K = 4M − 1, M ≥ 2 and equation; 2) K ≥ 4M, M ≥ 2 and N ≥ 2. where K,M,N respectively denotes the set size, number of channels, elementary sequence length of QCSS.

Key concepts: Aperiodic graph, Sequence (biology), Upper and lower bounds, Combinatorics, Set (abstract data type), Mathematics, Binary number, Weighting

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