Journal of the Korea Institute of Information and Communication Engineering (한국정보통신학회논문지)

The Korea Institute of Information and Commucation Engineering (한국정보통신학회)
권호 표지
DOI QR코드

DOI QR Code

Non-linear Extended Binary Sequence with Low Cross-Correlation

낮은 상호 상관관계를 갖는 비선형 확장 이진 수열

  • Received : 2011.12.27
  • Accepted : 2012.02.16
  • Published : 2012.04.30
Download PDF
⟨ Previous Next ⟩

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.

의사난수열은 코드 분할 다중접속과 같은 무선통신에서 중요한 역할을 한다. 여러 사용자가 동시에 시스템에 접속할 때 충돌이 발생 할 수 있는데, 의사난수열의 낮은 상관관계는 그런 통신시스템에서 다중 접속 간섭을 최소화 할 수 있다. 본 논문에서는 Welch bound의 관점에서 최적의 상호 상관관계 함숫값을 갖는 $m$-수열, GMW 수열, Kasami 수열, No 수열 등을 모두 포함하는 낮은 상호 상관관계를 갖는 비선형 확장 이진 수열군을 제안한다. 그리고 제안한 수열의 상호상관관계를 분석한다.

Keywords

References

  1. S.W. Golomb, "Shift Register Sequences," Holden Day, 1967.
  2. M.K. Simon, J.K. Omura, R.A. Scholtz, and B.K. Levitt, "Spread Spectrum Communications, Vol. 1, Rockville, MD: Computer Science Press," 1985.
  3. K. Fazel and S. Kaiser, "Multi-carrier and Spread Spectrum Systems," John Wiley and Sons Ltd., 2003.
  4. 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.
  5. 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.
  6. 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. https://doi.org/10.1016/0166-218X(85)90067-8
  7. R.A. Scholtz and R. Welch, "GMW sequences," IEEE Trans. Inform. Theory, Vol. IT-30, pp. 548-553, 1984.
  8. T. Kasami, "Weight distribution of Bose-Chaudhuri-Hocquenghem codes," in Combi- natorial Mathematics and Its Applications. Chapel Hill, NC: Univ. North Carolina Press, 1969.
  9. 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.
  10. 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.
  11. R. Prasad, "CDMA for Wireless Personal Communications," Artech House Publishers, 1996.
  12. R. Lidl and H. Niederreiter, "Finite Fields," Cambridge University Press 1997.
  13. L.R. Welch, "Lower bounds on the maximum cross-correlation of signals," IEEE Trans. Inform. Theory, vol. IT-20, pp. 397-399, 1974.
  14. 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. https://doi.org/10.1093/ietfec/e91-a.8.2263

Cited by

  1. 부분체를 이용한 비선형 수열의 상호상관관계의 효율적인 계산방법 vol.16, pp.8, 2012, https://doi.org/10.6109/jkiice.2012.16.8.1686