Constructions for almost perfect binary sequence pairs with even length

doi:10.21629/JSEE.2018.02.05

Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (2): 256-261.doi: 10.21629/JSEE.2018.02.05

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Constructions for almost perfect binary sequence pairs with even length

Xiuping PENG^1,³(), Hongbin LIN^2,*(), Jiadong REN¹(), Xiaoyu CHEN^1,³()

¹ School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China
² School of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China
³ Hebei Key Laboratory of Information Transmission and Signal Processing, Yanshan University, Qinhuangdao 066004, China

Received:2016-08-28 Online:2018-04-26 Published:2018-04-27
Contact: Hongbin LIN E-mail:pengxp@ysu.edu.cn;honphin@ysu.edu.cn;jdren@ysu.edu.cn;chenxiaoyu@ysu.edu.cn
About author:PENG Xiuping was born in 1984. She received her B.S. degree in communication engineering and her Ph.D. degree in circuit and system from Yanshan University, in 2008 and 2014, respectively. Currently, she is an adjunct professor in Yanshan University. Her research interests include sequence design and coding theory. E-mail: pengxp@ysu.edu.cn|LIN Hongbin was born in 1979. He received his B.S. degree in measurement & control technology and instrumentation, M.S. degree in measurement technology and automation and Ph.D. degree in circuit and system from Yanshan University, in 2003, 2006, and 2012, respectively. Currently, he is an adjunct professor in Yanshan University. His research interests include higher dimensional signal processing, pattern recognition and machine learning. E-mail: honphin@ysu.edu.cn|REN Jiadong was born in 1967. He received his B.S. and M.S. degrees in computer application technology from Northeast Heavy Machinery Institute, in 1989 and 1994, respectively, and Ph.D. degree in computer application technology in 1999 from Harbin Institute of Technology. Now, he is a professor at Yanshan University. His current major research interests include data mining and software security analysis. E-mail: jdren@ysu.edu.cn|CHEN Xiaoyu was born in 1983. She received her B.S. degree in communication engineering, M.S. degree in communication and information system and Ph.D. degree in circuit and system from Yanshan University, in 2006, 2010, and 2014, respectively. She is an adjunct professor in Yanshan University. Her major research interests include sequence design and network coding. E-mail: chenxiaoyu@ysu.edu.cn
Supported by:
the National Natural Science Foundation of China(61601401);the National Natural Science Foundation of China(61501395);the National Natural Science Foundation of China(61601399);the National Natural Science Foundation of China(61671402);Natural Science Foundation of Hebei Province(F2015203150);Natural Science Foundation of Hebei Province(F2016203293);Natural Science Foundation of Hebei Province(F2016203312);Natural Science Research Programs of Hebei Educational Committee(QN2016120);the Independent Research Programs for Young Teachers of Yanshan University(15LGB013);This work was supported by the National Natural Science Foundation of China (61601401; 61501395; 61601399; 61671402), Natural Science Foundation of Hebei Province (F2015203150; F2016203293; F2016203312), Natural Science Research Programs of Hebei Educational Committee (QN2016120) and the Independent Research Programs for Young Teachers of Yanshan University (15LGB013)

Abstract

Abstract:

The concept of the binary sequence pair is generalized from a single binary sequence. Binary sequence pairs are applied in many fields of radar, sonar or communication systems, in which signals with optimal periodic correlation are required. Several types of almost perfect binary sequence pairs of length T = 2q are constructed, where q is an odd number. These almost perfect binary sequence pairs are based on binary ideal sequence or binary ideal two-level correlation sequence pairs by using Chinese remainder theorem. For these almost perfect binary sequence pairs with good balanced property, their corresponding divisible difference set pairs (DDSPs) are also derived.

Key words: sequence design, divisible difference set pair (DDSP), binary sequence pair, almost perfect

Xiuping PENG, Hongbin LIN, Jiadong REN, Xiaoyu CHEN. Constructions for almost perfect binary sequence pairs with even length[J]. Journal of Systems Engineering and Electronics, 2018, 29(2): 256-261.

Figures/Tables 1

References 17

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Length	Out-of-phase correlation value	Method	Reference
$ T = pq, gcd(p, q) = 1 $	{–1}	Chinese remainder theorem	[11]
$ T = 4p, odd q $	{0, –4}	Cyclotomic classes	[11]
$ T = 1({\rm mod}\; 2) $	{1, –3}	Cyclic difference set (pair)	[12]
$ T = 3q, odd q > 3 $	{1, –3} or {–3, 1}	Cyclotomic classes	[13]
$ T = pq, {gcd}(p, q) = 1 $	{1, –3}	Chinese remainder theorem	[14]
$ T = 2q, q = 4f+1 and f is even $ $	{2, –2}	Cyclic almost difference set pair	[15]
$ T = 2q, odd q $	{0, –F}, the out-of-phase correlation value –F appears only once	Chinese remainder theorem	This paper

[1]	Cong Shuang & Lou Yuesheng. Design of control sequence of pulses for the population transfer of high dimensional spin 1/2 quantum systems [J]. Journal of Systems Engineering and Electronics, 2008, 19(6): 1226-1234.
[2]	Chen Gang & Zhao Zhengyu. Almost perfect sequences based on cyclic difference sets [J]. Journal of Systems Engineering and Electronics, 2007, 18(1): 155-159.

Constructions for almost perfect binary sequence pairs with even length

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