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Low Correlation Zone Sequences

(Invited Paper)
  • Jung-Soo Chung
  • Jong-Seon No
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6338)

Abstract

It is well known that low correlation zone sequences have been adopted as spreading sequences in the quasi-synchronous code division multiple access (QS-CDMA) systems of wireless communication systems, where time delay among different users is allowed to be within a few chips. In this paper, numerical analysis shows that the QS-CDMA systems using low correlation zone (LCZ) sequences outperform the conventional code division multiple access (CDMA) systems. Also, several LCZ sequences are revisited and a new extension method for the construction of LCZ sequences is proposed.

Keywords

Autocorrelation Code division multiple access (CDMA) Cross-correlation Low correlation zone (LCZ) sequence Pseudo noise (PN) sequence Quasi-synchronous code division multiple access (QS-CDMA) system Spreading sequence 

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References

  1. 1.
    Antweiler, M.: Cross-correlation of p-ary GMW sequences. IEEE Trans. Inf. Theory 40(4), 1253–1261 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Boztas, S., Kumar, P.V.: Binary sequences with Gold-like correlation but larger linear span. IEEE Trans. Inf. Theory 40(2), 532–537 (1994)zbMATHCrossRefGoogle Scholar
  3. 3.
    Boztas, S., Hammons, R., Kumar, P.V.: 4-phase sequences with near-optimum correlation properties. IEEE Trans. Inf. Theory 38(3), 1101–1113 (1992)zbMATHCrossRefGoogle Scholar
  4. 4.
    Chung, J.-S.: Properties of Sidel’nikov sequences and an extending method of LCZ sequence sets, Ph.D. dissertation, Seoul National Univ., Seoul, Korea (2010)Google Scholar
  5. 5.
    De Gaudenzi, R., Elia, C., Viola, R.: Bandlimited quasi-synchronous CDMA: A novel satellite access technique for mobile and personal communication systems. IEEE J. Sel. Areas Commun. 10(2), 328–343 (1992)CrossRefGoogle Scholar
  6. 6.
    Gold, R.: Maximal recursive sequences with 3-valued recursive crosscorrelation functions. IEEE Trans. Inf. Theory 14, 154–156 (1968)zbMATHCrossRefGoogle Scholar
  7. 7.
    Gordon, B., Mills, W.H., Welch, L.R.: Some new difference sets. Canadian J. Math. 14, 614–625 (1962)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Hall Jr., M.: A Survey of Difference Sets. Proc. Amer. Math. Soc. 7, 975–986 (1956)MathSciNetGoogle Scholar
  9. 9.
    Helleseth, T.: Some results about the cross-correlation function between two maximal linear sequences. Discrete Math. 16, 209–232 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Helleseth, T., Kumar, P.V.: Sequences with low correlation. In: Pless, V., Huffman, C. (eds.) Handbook of Coding Theory. Elsevier Science, Amsterdam (1998)Google Scholar
  11. 11.
    Hu, H., Gong, G.: New sets of zero or low correlation zone sequences via interleaving techniques. IEEE Trans. Inf. Theory 56(4), 1702–1713 (2010)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Jang, J.-W.: Families of sequences with optimal correlation property. Ph.D. dissertation, Seoul National Univ., Seoul, Korea (2006)Google Scholar
  13. 13.
    Jang, J.-W., Kim, S.-H., No, J.-S., Chung, H.: New constructions of quaternary Hadamard matrices. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 361–372. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Jang, J.-W., Kim, S.-H., No, J.-S.: New construction of quaternary low correlation zone sequence sets from binary low correlation zone sequence sets. Accepted for Publication in Journal of Communications and Networks (January 2010)Google Scholar
  15. 15.
    Jang, J.-W., Kim, Y.-S., No, J.-S., Helleseth, T.: New family of p-ary sequences with optimal correlation property and large linear span. IEEE Trans. Inf. Theory 50(8), 1839–1844 (2004)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Jang, J.-W., No, J.-S., Chung, H.: A new construction of optimal p 2-ary low correlation zone sequences using unified sequences. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E89-A(10), 2656–2661 (2006)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Jang, J.-W., No, J.-S., Chung, H.: Butson Hadamard matrices with partially cyclic core. Designs, Codes and Cryptography 43(2-3), 93–101 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Jang, J.-W., No, J.-S., Chung, H., Tang, X.: New sets of optimal p-ary low correlation zone sequences. IEEE Trans. Inf. Theory 53(2), 815–821 (2007)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Kim, S.-H.: Trace representation of Lempel-Cohn-Eastman sequences and new families of binary sequences with low correlation. Ph.D. dissertation, Seoul National Univ., Seoul, Korea (2004)Google Scholar
  20. 20.
    Kim, S.-H., Jang, J.-W., No, J.-S., Chung, H.: New constructions of quaternary low correlation zone sequences. IEEE Trans. Inf. Theory 51(4), 1469–1477 (2005)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Kim, S.-H., No, J.-S.: New families of binary sequences with low correlation. IEEE Trans. Inf. Theory 49(11), 3059–3065 (2003)CrossRefMathSciNetGoogle Scholar
  22. 22.
    Kim, Y.-S.: Properties of Sidel’nikov sequences and new sequence families with low correlation. Ph.D. dissertation, Seoul National Univ., Seoul, Korea (2007)Google Scholar
  23. 23.
    Kim, Y.-S., Jang, J.-W., No, J.-S., Chung, H.: New design of low correlation zone sequence sets. IEEE Trans. Inf. Theory 52(10), 4607–4616 (2006)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Kasami, T.: Weight distribution formular for some class of cyclic codes. Technical Report R-285 (AD 632574), Coordinated Science Laboratory, Univ. of Illinois, Urbana (April 1966)Google Scholar
  25. 25.
    Kasami, T.: Weight distribution of Bose-Chaudhuri-Hocquenghem codes. In: Cambinatorial Mathematics and Its Applications. Univ. of North Carolina Press, Chapel Hill (1969)Google Scholar
  26. 26.
    Kumar, P.V., Helleseth, T., Calderbank, A.R.: An upper bound for Weil exponential sums over Galois rings and applications. IEEE Trans. Inf. Theory 41(2), 456–468 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Kumar, P.V., Helleseth, T., Calderbank, A.R., Hammons Jr., A.R.: Large families of quaternary sequences with low correlation. IEEE Trans. Inf. Theory 42(2), 579–592 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Kumar, P.V., Liu, C.-M.: On lower bounds to the maximum correlation of complex roots-of unity sequences. IEEE Trans. Inf. Theory 36(3), 633–640 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Kumar, P.V., Moreno, O.: Prime-phase sequences with periodic correlation properties better than binary sequences. IEEE Trans. Inf. Theory 37, 603–616 (1991)CrossRefGoogle Scholar
  30. 30.
    Levenshtein, V.I.: Bounds on the maximal cardinality of a code with bounded modules of the inner product. Soviet. Math. Dokl. 25, 526–531 (1982)Google Scholar
  31. 31.
    Liu, S.-C., Komo, J.F.: Nonbinary Kasami sequences over GF(p). IEEE Trans. Inf. Theory 38, 1409–1412 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Long, B., Zhang, P., Hu, J.: A generalized QS-CDMA system and the design of new spreading codes. IEEE Trans. Veh. Technol. 47(4), 1268–1275 (1998)CrossRefGoogle Scholar
  33. 33.
    Moriuchi, T., Imamura, K.: Balanced nonbinary sequences with good periodic correlation properties obtained from modified Kumar-Moreno sequences. IEEE Trans. Inf. Theory 41, 572–576 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    No, J.-S.: p-ary unified sequences: p-ary extended d-form sequences with the ideal autocorrelation property. IEEE Trans. Inf. Theory 48(9), 2540–2546 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  35. 35.
    No, J.-S., Jang, J.-W.: Performance analysis of quasi-synchronous code division multiple access systems using new set of LCZ sequences. Telecommunications Review 15(3), 447–456 (2005)Google Scholar
  36. 36.
    No, J.-S., Kumar, P.V.: A new family of binary pseudorandom sequences having optimal correlation properties and large linear span. IEEE Trans. Inf. Theory 35, 371–379 (1989)zbMATHCrossRefGoogle Scholar
  37. 37.
    No, J.-S., Ryu, J.-H., Moon, J., Kim, S.-H., Kim, S., Jang, J.-W., Kim, S.-K., Go, J.-Y.: Research of Signal design and high efficiency modulation/channel code for 4G mobile access, ETRI (2002)Google Scholar
  38. 38.
    Olsen, J.D., Scholtz, R.A., Welch, L.R.: Bent-function sequences. IEEE Trans. Inf. Theory 28, 858–864 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  39. 39.
    Sarwate, D.V., Pursley, M.B.: Crosscorrelation properties of pseudorandom and related sequences. Proc. IEEE 68(5), 593–619 (1980)CrossRefGoogle Scholar
  40. 40.
    Scholtz, R., Welch, L.: GMW sequences. IEEE Trans. Inf. Theory 30(3), 548–553 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  41. 41.
    Sidel’nikov, V.M.: On mutual correlation of sequences. Soviet Math. Dokl. 12(1), 197–201 (1971)zbMATHGoogle Scholar
  42. 42.
    Tang, X.H., Fan, P.Z.: A class of pseudonoise sequences over GF(p) with low correlation zone. IEEE Trans. Inf. Theory 47(4), 1644–1649 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  43. 43.
    Tang, X.H., Fan, P.Z., Matsufuji, S.: Lower bounds on correlation of spreading sequence set with low or zero correlation zone. Electron. Lett. 36(6), 551–552 (2000)CrossRefGoogle Scholar
  44. 44.
    Torii, H., Nakamura, M., Suehiro, N.: A new class of zero-correlation zone sequences. IEEE Trans. Inf. Theory 50(3), 559–565 (2004)CrossRefMathSciNetGoogle Scholar
  45. 45.
    Trachtenberg, H.M.: On the cross-correlation functions of maximal recurring sequences. Ph.D. dissertation, Univ. of Southern California, Los Angeles, CA (1970)Google Scholar
  46. 46.
    Udaya, P.: Polyphase and frequency hopping sequences obtained from finite rings. Ph.D. dissertation, Indian Inst. Technol, Kanpur, India (1992)Google Scholar
  47. 47.
    Wang, J.-S., Qi, W.-F.: Analysis of designing interleaved ZCZ sequence families. In: Gong, G., Helleseth, T., Song, H.-Y., Yang, K. (eds.) SETA 2006. LNCS, vol. 4086, pp. 129–140. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  48. 48.
    Welch, L.R.: Lower bounds on the maximum cross correlation of signals. IEEE Trans. Inf. Theory 20, 397–399 (1974)zbMATHCrossRefMathSciNetGoogle Scholar
  49. 49.
    Yang, J.-D., Jin, X., Song, K.-Y., No, J.-S., Shin, D.-J.: Multicode MIMO systems with quaternary LCZ and ZCZ sequences. IEEE Trans. Veh. Technol. 57(4), 2334–2341 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jung-Soo Chung
    • 1
  • Jong-Seon No
    • 1
  1. 1.Department of Electrical Engineering and Computer Science, Institute of New Media and CommunicationsSeoul National UniversitySeoulKorea

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