DOI QR코드

DOI QR Code

Computing Method of Cross-Correlation of Non-Linear Sequences Using Subfield

부분체를 이용한 비선형 수열의 상호상관관계의 효율적인 계산방법

  • Received : 2012.03.12
  • Accepted : 2012.04.30
  • Published : 2012.08.31

Abstract

Spreading sequence play an important role in wireless communications, such as in a CDMA(code division multiple access) communication system and multi-carrier spectrum communication system. Spreading sequences with low cross-correlation, in a direct-sequence spread spectrum communication system, help to minimize multiple access interference and to increase security degree of system. Analysis of cross-correlations between the sequences is a necessary process to design sequences. However it require lots of computing time for analysis of cross-correlations between sequences. In this paper we propose a method which is possible to compute effectively cross-correlation using subfield in the process of practical computation of cross-correlation between nonlinear binary sequences.

확산수열(spreading sequence)은 다중 반송파 대역확산(multi-carrier spectrum) 통신시스템과 CDMA와 같은 무선통신에서 중요한 역할을 한다. 이러한 통신 시스템에서 낮은 상호상관관계를 갖는 확산수열은 다중접속 충돌을 최소화하고, 시스템의 보안수준을 가능한 높일 수 있다. 수열을 설계하는 데 있어 상호상관관계를 분석한는 것을 반드시 필요한 절차이다. 상호상관관계를 분석하기 위해서는 많은 계산 시간이 요구된다. 본 논문에서는 비선형 이진수열의 상호상관관계를 실제적으로 계산하는 과정에서 부분체를 이용하여 효과적으로 구하는 방법을 제안한다.

Keywords

References

  1. 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 Netherlands: North-Holland, Vol. II, pp. 1765-1853, 1998.
  2. 최언숙, 조성진, 권숙희, "낮은 상호 상관관계를 갖는 비선형 확장 이진 수열", 한국정보통신학회논문지, Vol.16(4), pp.730-736, 2012. https://doi.org/10.6109/jkiice.2012.16.4.730
  3. S.W. Golomb, "On the classification of balanced binary sequences of period $2^{n}-1$", IEEE Trans. Inform. Theory, Vol. IT-26(6), pp. 730-732, 1980.
  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. S.W. Golomb, Shift Register Sequences, Holden Day, 1967.
  6. R.A. Scholtz and R. Welch, "GMW sequences", IEEE Trans. Inform. Theory, Vol. IT-30, pp. 548-553, 1984.
  7. 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.
  8. L.R. Welch, "Lower bounds on the maximum crosscorrelation of signals", IEEE Trans. Inform. Theory, Vol. IT-20, pp. 397-399 1974.
  9. T. Kasami, "Weight distribution formula for some class of cyclic codes", Coordinated Science Laboratory, University of Illionos, Urbana, Tech. Rep. R-285 (AD632574), 1966.
  10. T. Helleseth, J. Lahtonen and P. Rosendahl, "On Niho type cross-correlation functions of m-sequences", Finite Fields and Their Applications, Vol. 13, pp. 305-317, 2007. https://doi.org/10.1016/j.ffa.2005.09.004
  11. A.M. Klapper, "d-form sequences: families of sequences with low correlation values and large linear spans", IEEE Trans. Inform. Theory, Vol. 41, pp. 423-431, 1995. https://doi.org/10.1109/18.370143
  12. R. Prasad, CDMA for Wireless Personal Communications, Artech House Publishers, 1996.
  13. D. Guo, L.K. Rasmussen and T.J. Lim, " Linear Parallel Interference Cancellation in Long-code CDMA Multiuser Detection", IEEE J. Selected Areas in Communications, Vol. 17, pp. 2074 - 2081, 1999. https://doi.org/10.1109/49.814805
  14. R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press, 1997.
  15. U.S. Choi, S.J. Cho and S.H. Kwon, "Analysis of cross-correlation of extended non-linear binary sequences" (To appear).