한국전자통신학회논문지 (The Journal of the Korea institute of electronic communication sciences)

한국전자통신학회 (Korea Institute of Electronic Communication Science)
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최적의 상호상관관계를 갖는 이진 수열의 설계

Design of Binary Sequences with Optimal Cross-correlation Values

  • 투고 : 2011.07.07
  • 심사 : 2011.08.12
  • 발행 : 2011.08.31
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⟨ 이전 논문 다음 논문 ⟩

초록

적당한 정수 $n({\geq}1)$에 대하여 2-valued 자기상관관계를 갖는 주기가 $2^n-1$인 균형 이진 수열(balanced binary sequences)은 대역확산 통신 시스템(spread-spectrum communication system)에서 많이 응용되고 있다. 본 논문에서는 르장드르 수열에 의해 구성되는 새로운 3-valued 비선형 이진 수열을 제안한다. 이 수열은 유한체 위에서 트레이스를 이용해 생성하는 가장 우수한 수열인 m-수열, GMW 수열, Kasami 수열, No 수열을 모두 포함한다. 제안된 수열은 Klapper에 의해 제안된 이차형식 수열보다 더 낮은 상호상관관계를 갖는다.

Balanced binary sequences of period $2^n-1(n{\geq}1)$ having the two-valued autocorrelation function have many applications in spread-spectrum communications system. In this paper we propose new nonlinear binary sequences which are constructed from Legendre sequences with the same cross-correlation as the sequences proposed by Cho. These sequences include the m-sequences, GMW sequences, Kasami sequences and No sequences which are described in terms of the trace function over a finite field. Also the proposed sequences have more low cross-correlation distribution than the quadratic form sequences proposed by Klapper.

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참고문헌

  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 Vetherland: North-Holland, Vol. II, pp. 1765-1853, 1998.
  2. 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.
  3. S.W. Golomb, "On the classification of balanced binary sequences of period $2^{n}-1$," IEEE trans. Inform. Theory, Vol. IT-26, No.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, H.K. Lee, H. Chuang, H.Y. Song, and K. Yang, "Trace representation of Legendre Sequences of Mersenne prime period," IEEE Trans. Inform. Theory, Vol. 42, No. 6, pp. 2254-2255, 1996. https://doi.org/10.1109/18.556617
  8. 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, No. 2, pp. 371-379, 1989.
  9. T. Kasami, "Weight distribution of Bose- Chaudhuri-Hocquenghem codes," in Combinatorial Mathematics and Its Applications. Chapel Hill, NC: Univ. North Carolina Press, 1969.
  10. A. Klapper, "Large Families of Sequences with Near-Optimal Correlations and Large Linear Span," IEEE Trans. Inform. Theory, Vol. 42, No. 4, pp. 1241-1248, 1996. https://doi.org/10.1109/18.508849
  11. U.S. Choi, S.J. Cho, H.D. Kim, "Attack using Phase Shifts of Shrunken Sequence", J. The Korea Institute of Electronic Communication Sciences, Vol. 6, No. 1, pp. 97-104, 2011.
  12. J.G. Kim, S.J. Cho, U.S. Choi, Y.H. Hwang, " Crosscorrelation of Kasami sequences and No sequences", J. The Korea Institute of Electronic Communication Sciences, Vol. 6, No. 1, pp. 13-19, 2011.
  13. U.S. Choi, S.J. Cho, J.G. Kim, " Analysis of Shrunken Sequences using LFSR and CA on $GF(2^{P})$", J. The Korea Institute of Electronic Communication Sciences, Vol. 5, No. 4, pp. 418-424, 2010.
  14. S.J. Cho, U.S. Choi, H.D. Kim, H.J. An, " Analysis of nonlinear sequences based on shrinking generator", J. The Korea Institute of Electronic Communication Sciences, Vol. 5, No. 4, pp. 412-417, 2011.
  15. S.J. Cho, S.H. Kwon, "A new family binary sequences with low correlation," (submitted).
  16. L.R. Welch, "Lower bounds on the maximum cross-correlation of signals," IEEE Trans. Inform. Theory, Vol. IT-20, pp. 397-399, 1974.
  17. R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press 1997.
  18. J.S. No, "p-ary unified sequences : p-ary extended d-form sequences with ideal autocorrelation property," IEEE Trans. Inform. Theory, Vol. 48, No. 9, pp. 2540-2546, 2002. https://doi.org/10.1109/TIT.2002.801406