Browse > Article
http://dx.doi.org/10.6109/jkiice.2012.16.4.730

Non-linear Extended Binary Sequence with Low Cross-Correlation  

Choi, Un-Sook (동명대학교)
Cho, Sung-Jin (부경대학교)
Kwon, Sook-Hee (부경대학교)
Publication Information
Journal of the Korea Institute of Information and Communication Engineering / v.16, no.4, 2012 , pp. 730-736 More about this Journal
Abstract
PN(Pseudo Noise) sequences play an important role in wireless communications, such as in a CDMA(code division multiple access) communication system. If there is a crash when multiple users simultaneously connected to a system, then PN sequences with low correlation help to minimize multiple access interference in such communication system. In this paper we propose a family of non-linear extended binary sequences with low cross-correlations and the family include $m$-sequence, GMW sequence, Kasami sequence and No sequence with optimal cross-correlation in terms of Welch bound. And we analyze cross-correlation of these sequences.
Keywords
CDMA; correlation; $m$-sequence; non-linear binary sequence; trace;
Citations & Related Records
연도 인용수 순위
  • Reference
1 L.R. Welch, "Lower bounds on the maximum cross-correlation of signals," IEEE Trans. Inform. Theory, vol. IT-20, pp. 397-399, 1974.
2 F.X. Zeng and Z.Y. Zhang, "Several Families of Sequences with Low Correlation and Large Linear Span", IEEE Trans. Fundamentals. vol. E91-A, pp. 2263-2268, 2008.   DOI   ScienceOn
3 S.W. Golomb, "Shift Register Sequences," Holden Day, 1967.
4 M.K. Simon, J.K. Omura, R.A. Scholtz, and B.K. Levitt, "Spread Spectrum Communications, Vol. 1, Rockville, MD: Computer Science Press," 1985.
5 K. Fazel and S. Kaiser, "Multi-carrier and Spread Spectrum Systems," John Wiley and Sons Ltd., 2003.
6 T. Helleseth and P.V. Kumar, "Sequences with low correlation," in Handbook of Coding Theory, V.S. Pless and W.C. Huffman, Eds., Amsterdam, The Vetherland: North-Holland, Vol. II, pp.1765-1853, 1998.
7 T. Kasami, "Weight distribution of Bose-Chaudhuri-Hocquenghem codes," in Combi- natorial Mathematics and Its Applications. Chapel Hill, NC: Univ. North Carolina Press, 1969.
8 G. Gong, "New designs for signal sets with low cross correlation, balance property, and large linear span: GF(p) case," IEEE trans. Inform. Theory, Vol. 4, pp. 2847-2867, 2002.
9 R.A. Games, "Cross correlation of m-sequences and GMW sequences with the same primitive polynomial", Discrete Appl. Math. Vol. 12, pp. 139-146, 1985.   DOI   ScienceOn
10 R.A. Scholtz and R. Welch, "GMW sequences," IEEE Trans. Inform. Theory, Vol. IT-30, pp. 548-553, 1984.
11 J.S. No, and P.V. Kumar, "A new family of binary pseudorandom sequences having optimal periodic correlation properties and large linear span," IEEE Trans. Inform. Theory, Vol. IT-35(2), pp. 371-379, 1989.
12 N. Yee, J-P. Linnartz and G. Fettweis, "Multi-carrier CDMA in indoor wireless Radio Networks," Proc. of IEEE PIMRC '93, Yokohama, Japan, Sept. 1993, pp. 109-13.
13 R. Prasad, "CDMA for Wireless Personal Communications," Artech House Publishers, 1996.
14 R. Lidl and H. Niederreiter, "Finite Fields," Cambridge University Press 1997.