Skip to main content
SpringerLink
Log in

Construction of low-hit-zone frequency hopping sequences with optimal partial Hamming correlation by interleaving techniques

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

In quasi-synchronous frequency hopping code division multiple-access systems, frequency hopping sequences (FHSs) with low-hit-zone (LHZ) are commonly employed to minimize multiple-access interferences. Usually, the length of correlation window is shorter than the period of the chosen FHSs due to the limited synchronization time or hardware complexity. Thus the study of the partial Hamming correlation properties of LHZ FHSs is of particular importance. In this paper, we prove the nonexistence of LHZ FHS sets with strictly optimal partial Hamming correlation in some conditions. In addition, employing the interleaving techniques, we present a construction of LHZ FHS sets with optimal partial Hamming correlation from m-sequences. The fundamental idea of our design is to use short individual m-sequences together with certain appropriate shift sequences to construct long LHZ FHS sets with optimal partial Hamming correlation. In particular, our construction gives new parameters not covered in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Cai H., Zhou Z.C., Yang Y., Tang X.H.: A new construction of frequency-hopping sequences with optimal partial Hamming correlation. IEEE Trans. Inf. Theory 60, 5782–5789 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen H.H.: The Next Generation CDMA Technologies. Wiley, London (2007).

    Book  Google Scholar 

  3. Chung J.-H., Yang K.: New classes of optimal low-hit-zone frequency-hopping sequence sets by Cartesian product. IEEE Trans. Inf. Theory 59, 726–732 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  4. Chung J.-H., Han Y., Yang K.: New classes of optimal frequency-hopping sequences by interleaving techniques. IEEE Trans. Inf. Theory 55, 5783–5791 (2009).

    Article  MathSciNet  Google Scholar 

  5. Ding C., Fuji-Hara R., Fujiwara Y., Jimbo M., Mishima M.: Sets of frequency hopping sequences: bounds and optimal constructions. IEEE Trans. Inf. Theory 55, 3297–3304 (2009).

    Article  MathSciNet  Google Scholar 

  6. Ding C., Yang Y., Tang X.: Optimal sets of frequency hopping sequences from linear cyclic codes. IEEE Trans. Inf. Theory 56, 3605–3612 (2010).

    Article  MathSciNet  Google Scholar 

  7. Eun Y.C., Jin S.Y., Hong Y.P., Song H.Y.: Frequency hopping sequences with optimal partial autocorrelation properties. IEEE Trans. Inf. Theory 50, 2438–2442 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  8. Fan P.Z., Darnell M.: Sequence Design for Communications Applications. Research Studies Press (RSP). Wiley, London (1996).

    Google Scholar 

  9. Fan P.Z., Lee M.H., Peng D.Y.: New family of hopping sequences for time/frequency-hopping CDMA systems. IEEE Trans. Wireless Commun. 4, 2836–2842 (2005).

    Article  Google Scholar 

  10. Gaudenzi R.D., 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, 328–343 (1992).

    Article  Google Scholar 

  11. Ge G., Miao Y., Yao Z.: Optimal frequency hopping sequences: Auto- and cross-correlation properties. IEEE Trans. Inf. Theory 55, 867–879 (2009).

    Article  MathSciNet  Google Scholar 

  12. Golomb S.W., Gong G.: Signal Design for Good Correlation: For Wireless Communication, Cryptography and Radar. Cambridge University Press, Cambridge (2005).

    Book  MATH  Google Scholar 

  13. Gong G.: Theory and applications of \(q\)-ary interleaved sequences. IEEE Trans. Inf. Theory 41, 400–411 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  14. Gong G.: New designs for signal sets with low cross correlation, balance property and large linear span: GF(\(p\)) case. IEEE Trans. Inf. Theory 48, 2847–2867 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  15. Gong G., Song H.Y.: Two-tuple balance of non-binary sequences with ideal two-level autocorrelation. Discret. Math. 154, 2590–2598 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  16. Han H.Y., Peng D.Y., Liu X.: On the average Hamming correlation of frequency hopping sequences. IEICE Trans. Fundam. 97, 1430–1433 (2014).

    Article  Google Scholar 

  17. Han H.Y., Peng D.Y., Liu X.: On low-hit-zone frequency-hopping sequence sets with optimal partial Hamming correlation. In: Proceedings of the 8th International Conference on Sequences and Their Applications, pp. 293–304 (2014).

  18. Lempel A., Greenberger H.: Families of sequences with optimal Hamming correlation properties. IEEE Trans. Inf. Theory 20, 90–94 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  19. Liu X., Peng D.Y., Han H.Y.: Low-hit-zone frequency hopping sequence sets with optimal partial Hamming correlation properties. Des. Codes Cryptogr. 73, 167–176 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  20. Ma W.P., Sun S.H.: New designs of frequency hopping sequences with low hit zone. Des. Codes Cryptogr. 60, 145–153 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  21. Niu X.H., Peng D.Y., Liu F., Liu X.: Lower bounds on the maximum partial correlations of frequency hopping sequence set with low hit zone. IEICE Trans. Fund. Electron. Commun. Comput. Sci. 93, 2227–2231 (2010).

    Google Scholar 

  22. Niu X.H., Peng D.Y., Zhou Z.C.: New classes of optimal low hit zone frequency hopping sequences with new parameters by interleaving technique. IEICE Trans. Fund. Electron. Commun. Comput. Sci. 95, 1835–1842 (2012).

    Google Scholar 

  23. Niu X.H., Peng D.Y., Zhou Z.C.: Frequency/time hopping sequence sets with optimal partial Hamming correlation properties. Sci. China Ser. F 55, 2207–2215 (2012).

    MathSciNet  MATH  Google Scholar 

  24. Niu X.H., Peng D.Y., Zhou Z.C.: New classes of optimal frequency hopping sequences with low hit zone. Adv. Math. Commun. 7, 293–310 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  25. Parampalli U., Siddiqi M.U.: Optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings. IEEE Trans. Inf. Theory 44, 1492–1503 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  26. Peng D.Y., Fan P.Z.: Lower bounds on the Hamming auto- and cross correlations of frequency-hopping sequences. IEEE Trans. Inf. Theory 50, 2149–2154 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  27. Peng D.Y., Fan P.Z., Lee M.H.: Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone. Sci. China Ser. F 49, 1–11 (2006).

    MathSciNet  MATH  Google Scholar 

  28. Wang X.N., Fan P.Z.: A class of frequency hopping sequences with no hit zone. In: Proceedings of the 4th International Conference on Parallel and Distributed Computing, Applications and Technologies, pp. 896–898 (2003).

  29. Wang C.Y., Peng D.Y., Han H.Y., Zhou L.M.N.: New sets of low-hit-zone frequency-hopping sequence with optimal maximum periodic partial Hamming correlation. Sci China Inf. Sci. 58, 1–15 (2015).

    Google Scholar 

  30. Zeng X., Cai H., Tang X.H., Yang Y.: A class of optimal frequency hopping sequences with new parameters. IEEE Trans. Inf. Theory 58, 4899–4907 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  31. Zhou Z.C., Tang X.H., Gong G.: A new class of sequences with zero or low correlation zone based on interleaving technique. IEEE Trans. Inf. Theory 54, 4267–4273 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  32. Zhou Z.C., Tang X.H., Niu X.H., Parampalli U.: New classes of frequency-hopping sequences with optimal partial correlation. IEEE Trans. Inf. Theory 58, 453–458 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  33. Zhou Z.C., Tang X.H., Peng D.Y., Parampalli U.: New constructions for optimal sets of frequency-hopping sequences. IEEE Trans. Inf. Theory 57, 3831–3840 (2011).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Science Foundation of China (Grant No. 61271244), the National Science Foundation of China (Grant No. 61571373), the National High Technology Research and Development Program of China (863 Program) (Grant No. 2015AA01A705), the Communications Sensing and Coding Research Network, the International Research and Research Training Fund, the University of Melbourne and the ARC Discovery (Grant No. DP150104473).

Author information

Authors and Affiliations

  1. School of Computer Science, Sichuan Normal University, Chengdu, China

    Hongyu Han

  2. School of Information Science and Technology, Southwest Jiaotong University, Chengdu, China

    Daiyuan Peng & Zheng Ma

  3. Department of Computing and Information Systems, University of Melbourne, Melbourne, VIC, Australia

    Udaya Parampalli

  4. School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, China

    Hongbin Liang

Authors
  1. Hongyu Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daiyuan Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Udaya Parampalli
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zheng Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hongbin Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongyu Han.

Additional information

Communicated by D. Jungnickel.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Han, H., Peng, D., Parampalli, U. et al. Construction of low-hit-zone frequency hopping sequences with optimal partial Hamming correlation by interleaving techniques. Des. Codes Cryptogr. 84, 401–414 (2017). https://doi.org/10.1007/s10623-016-0274-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-016-0274-8

Keywords

Mathematics Subject Classification

Search

Navigation