The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
권호 표지

Construction Method of Binary Low Correlation Zone Sequence Set Using Gray Mapping

Gray 사상을 이용한 이진 낮은 상관구역 수열군의 생성법

  • Published : 2009.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we propose a new construction method of binary low correlation zone (LCZ) sequence set. New construction method applies Gray mapping to conventional quaternary LCZ sequence set that has specific property. The period of new binary sequence set is twice as that of used sequence set in construction, and maximum magnitude of correlation value within the LCZ and cardinality of new set is also twice as those of used quaternary sequence set. But the LCZ size is the same with that of used sequence set. If the used Quaternary sequence set is optimal, the constructed binary sequence set is optimal with high probability.

본 논문에서는 이진 낮은 상관 구역 수열군의 새로운 생성법을 제안한다. 새로운 수열군은 Kim과 Jang, No, Chung이 제안한 4진 낮은 상관 구역 수열군에 Gray 사상을 적용하여 생성한다. 새로 생성된 이진 수열군의 주기는 생성에 사용한 4진 수열군의 주기의 2배이며, 낮은 상관구역 내 상관 값의 최대 크기 및 수열군의 크기는 생성에 사용한 수열군의 그것의 2배가 된다. 그러나 낮은 상관 구역의 크기는 그대로 유지된다. 생성에 사용한 4진 낮은 상관 구역 수열군의 최적인 경우 새로 생성된 이진 수열군은 높은 확률로 최적의 수열군이 된다.

Keywords

References

  1. R. De Gaudenzi, C. Elia, and R. Viola, "Bandlimited quasi-synchronous CDMA: A novel satellite access technique for mobile and personal communication systems," IEEE J. Sel. Areas Commun., Vol.10, No.2, pp.328-343, Feb. 1992 https://doi.org/10.1109/49.126984
  2. B. Long, P. Zhang, and J. Hu, 'A generalized QS-CDMA system and the design of new spreading codes,' IEEE Trans. Veh. Technol., Vol.47, No.6, pp.1268-1275, Nov. 1998 https://doi.org/10.1109/25.728516
  3. J.-D. Yang, X. Jin, K.-Y. Song, J.-S. No, and D.-J. Shin, 'Multicode MIMO systems with quaternary LCZ and ZCZ sequences,' IEEE Trans. Veh. Technol., Vol.57, No.4, pp.2334-2341, July 2008 https://doi.org/10.1109/TVT.2007.914059
  4. J.-H. Chung and K. Yang, 'New design of quaternary low-correlation zone sequence sets and quaternary Hadamard matrices,' IEEE Trans. Inf. Theory, Vol.54, No.8, Aug. 2008 https://doi.org/10.1109/TIT.2008.926406
  5. J.-W. Jang, J.-S. No, and H. Chung, "A new construction of optimal $p^{2}$-ary low correlation zone sequences using unified sequences," IEICE Trans. Fundamentals, Vol.E89-A, No.10, pp.2656-2661, Oct. 2006 https://doi.org/10.1093/ietfec/e89-a.10.2656
  6. J.-W. Jang, J.-S. No, H. Chung, and X. Tang, "New sets of optimal $p$-ary low correlation zone sequences," IEEE Trans. Inf. Theory, Vol.53, No.2, pp.815-821, Feb. 2007 https://doi.org/10.1109/TIT.2006.889715
  7. Y.-S. Kim, J.-W. Jang, J.-S. No, and H. Chung, 'New design of low correlation zone sequence sets,' IEEE Trans. Inf. Theory, Vol.52, No.10, pp.4607-4616, Oct. 2006 https://doi.org/10.1109/TIT.2006.881730
  8. S.-H. Kim, J.-W. Jang, J.-S. No, and H. Chung, 'New constructions of quaternary low correlation zone sequences,' IEEE Trans. Inf. Theory, Vol.51, No.4, pp.1469-1477, Apr.2005 https://doi.org/10.1109/TIT.2005.844068
  9. X. H. Tang and P. Z. Fan, "A class of pseudonoise sequences over $GF\left(p \right)$ with low correlation zone," IEEE Trans. Inf. Theory, Vol.47, No.4, pp.1644-1649, May 2001 https://doi.org/10.1109/18.923753
  10. X. H. Tang, P. Z. Fan, and S. Matsufuji, 'Lower bounds on correlation of spreading sequence set with low or zero correlation zone,' Electron. Lett., Vol.36, No.6, pp.551-552, Mar. 2000 https://doi.org/10.1049/el:20000462
  11. J. S. Cha, S. Kameda, K. Takahashi, M. Yokoyama, N. Suehiro, K. Masu, K. Tsubouchi, 'Proposal and Implementation of Approximately synchronized CDMA system using novel biphase sequences,' Proc. IEICE ITC-CSCC 99, Sado Island Japan, Vol.1, pp.56-59, July. 1999
  12. J.S. Cha, S. Kameda, M. Yokoyama, H. Nakase, K. Masu and K. Tsubouchi, 'New binary sequences with zero-correlation duration for approximately synchronised CDMA,' Electron. Lett., Vol.36, issue 11, pp.991-993, 2000 https://doi.org/10.1049/el:20000703
  13. J.S. Cha, 'Class of ternary spreading sequences with zero correlation duration,' Electron. Lett., Vol.37, issue10, pp.636-637, 2001 https://doi.org/10.1049/el:20010450
  14. S.-Y. Lee, J. S. Cha, J.-W. Seo, E.-Y. Ko, and M.-C. Shin, 'A class of multi-phase ZCD sequqnces for MAI-Cancelled DS-CDMA Systems,' Proc. ICIS 2002, Seoul , Korea, Vol.1, 2002, pp.817-820
  15. C. E. Lee, "Perfect $q$-ary sequences from multiplicative characters over $GF\left(p \right)$," Electron. Lett., Vol.28, pp.833-835, 1992 https://doi.org/10.1049/el:19920527
  16. V. M. Sidel'nikov, 'Some $k$-valued pseudo-random sequences and nearly equidistant codes,' Probl. Inf. Transm., Vol.5, No.1, pp.12-16, 1969.
  17. J.-S. No, K. Yang, H. Chung, and H.-Y. Song, 'On the construction of binary sequences with ideal autocorrelation property,' in Proc. IEEE Int. Symp. Inform. Theory and Its Appl. (ISITA'96), Victoria, British Columbia, Canada, Sep. 1996, pp.837-840