Binary Sequence Pairs With Two-level Autocorrelation Functions

Xu, Chengqian; Liu, Kai; Li, Gang; Yu, Wangbo

doi:10.1109/wicom.2007.345

Cited by 5 publications

(6 citation statements)

References 3 publications

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“…By virtue of the transformations of Sect. 2 we assume without loss of generality v/2 ≥ k a ≥ k b ≥ k and in that case k − λ ≥ 0 by (12)…”

Section: Ideal Cyclic Difference Pairsmentioning

confidence: 99%

“…In 2007, it is constructed [12] by Xu, et al a class of binary sequence pairs of length v having a two-level correlation where v = 2n 2 − 1, Γ 1 = 2n 2 − 8n + 11 and Γ 2 = 2n 2 − 8n + 7, for every positive integer n. Note that |Γ 1 − Γ 2 | = 4. The authors of this paper presented [13] in 2008 a class of binary sequence pairs of length v with an ideal two-level correlation where v = 4u, Γ 1 = 4 and Γ 2 = 0 for every positive integer u.…”

Section: Introductionmentioning

confidence: 99%

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Binary Sequence Pairs with Two-Level Correlation and Cyclic Difference Pairs

Jin

Song

2010

IEICE Trans. Fundamentals

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We investigate binary sequence pairs with two-level correlation in terms of their corresponding cyclic difference pairs (CDPs). We define multipliers of a cyclic difference pair and present an existence theorem for multipliers, which could be applied to check the existence/nonexistence of certain hypothetical cyclic difference pairs. Then, we focus on the ideal case where all the out-of-phase correlation coefficients are zero. It is known that such an ideal binary sequence pair exists for length v = 4u for every u ≥ 1. Using the techniques developed here on the theory of multipliers of a CDP and some exhaustive search, we are able to determine that, for lengths v ≤ 30, (1) there does not exist "any other" ideal binary sequence pair and (2) every example in this range is equivalent to the one of length v = 4u above. We conjecture that if there is a binary sequence pair with an ideal two-level correlation then its in-phase correlation must be 4. This implies so called the circulant Hadamard matrix conjecture.

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“…By virtue of the transformations of Sect. 2 we assume without loss of generality v/2 ≥ k a ≥ k b ≥ k and in that case k − λ ≥ 0 by (12)…”

Section: Ideal Cyclic Difference Pairsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Binary Sequence Pairs with Two-Level Correlation and Cyclic Difference Pairs

Jin

Song

2010

IEICE Trans. Fundamentals

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“…From (7) and (8), the correlation property between arbitrary two sequence pairs (f r ,g r ) and (f s ,g s ) in the set {(f r ,g r )}is following: (10,9,8,7,6,5,4,3). By (7), an orthogonal sequence pair set {(f r ,g r )} 7 0 = r with length 12 from sequence pair (w,t) is constructed , including 8 sequence pairs such as (f 0 , g 0 ) and (f 1 , g 1 ) with f 0 = (-++---------), g 0 = (-++-+-+-+-+-) and f 1 = (--++--------), g 1 = (+-++-+-+-+--), "+" and "-" denoting +1 and -1 respectively.…”

Section: Constructionmentioning

confidence: 99%

“…Some binary ZCZ sequence pair sets, but with some zeros in the sequences, have been presented by Krengel , Quang Khai Trinh and Pingzhi Fan from almost-perfect binary and almost-perfect ternary sequences and mismatched filtering [5], [6]. The difference set pairs, a new concept of combinatorial mathematics, have been proposed and applied to sequence design [1] [4]. In this paper, depending on difference set pairs, a new construction of binary ZCZ sequence pair sets, with entirely binary sequence compared to those current binary ZCZ sequence pair sets.…”

Section: Introductionmentioning

confidence: 99%

Binary Zero Correlation Zone Sequence Pair Set Constructed from Difference Set Pairs

Liu

2009

2009 International Conference on Networks Security, Wireless Communications and Trusted Computing

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This paper proposes a new construction method of binary sequence pair sets with zero correlation zone (ZCZ) in which the correlation functions of sequence pairs are zero, based on difference set pair, a new concept of combinatorial mathematics. With the extension of sequence length, the sets achieve the theoretical upper bound. These ZCZ sequence pairs can be applied to the generalized quasi-synchronous multiple-access system (QS-CDMA) to reduce and eliminate multiple access interference and co-channel interference.

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“…Xu and Jin have proposed binary sequence pairs with two-level (BSPT) periodic autocorrelation function in [10] and [11] respectively. And a variety of lengths of BSPTs are also constructed, such as (mn-1), (4n), (6n-1), (2n 2 -1), etc.…”

Section: Introductionmentioning

confidence: 99%

Binary sequence pair based time-domain superimposed training for OFDM

Shi

Jin

Fang

et al. 2013

2013 IEEE Wireless Communications and Networking Conference (WCNC)

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This paper introduces a class of perfect binary sequence pair (PBSP), which is characterized by the impulseequivalent periodic autocorrelation function (PACF) and the length of N=2 k . The proposed PBSP can be generated from a class of difference set pairs (DSP). Considering the desirable properties of the proposed sequence pair, orthogonal frequency division multiplexing (OFDM) transmission with time-domain superimposed training is proposed. Simulation results show that our binary sequence pair is ideal for channel estimation in terms of complexity, accuracy and efficiency.

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Binary Sequence Pairs With Two-level Autocorrelation Functions

Cited by 5 publications

References 3 publications

Binary Sequence Pairs with Two-Level Correlation and Cyclic Difference Pairs

Binary Sequence Pairs with Two-Level Correlation and Cyclic Difference Pairs

Binary Zero Correlation Zone Sequence Pair Set Constructed from Difference Set Pairs

Binary sequence pair based time-domain superimposed training for OFDM

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