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Constructions of optimal low-hit-zone frequency hopping sequence sets

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Abstract

In recent years, the study relating to low-hit-zone frequency hopping sequence sets, including the bounds on the Hamming correlations within the low hit zone and the optimal constructions, has become a new research area attracting the attention of many related researchers. In this paper, two constructions of optimal frequency hopping sequence sets with low hit zone have been employed, one of which is based on m-sequence while the other is based on the decimated sequences of m-sequence. Moreover, in the special case of \(k=n-1\), the construction based on the decimated sequences of m-sequence also yields low-hit-zone frequency hopping sequence sets with optimal periodic partial Hamming correlation property.

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References

  1. Chung J., 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 

  2. Ding C., Yin J.: Sets of optimal frequency-hopping sequences. IEEE Trans. Inf. Theory 54, 3741–3745 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  3. 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  MATH  Google Scholar 

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

    Google Scholar 

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

    Book  MATH  Google Scholar 

  6. Han H., Peng D., Liu X.: On low-hit-zone frequency hopping sequence sets with optimal partial Hamming correlation. In: SETA 2014. Lecture Notes in Computer Science, vol. 8865, pp. 293–304. Springer, Berlin (2014).

  7. 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 

  8. Liu X., Peng D., Han H.: 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 

  9. Ma W., Sun S.: New designs of frequency hopping sequences with low hit zone. Des. Codes Cryptogr. 60, 145–153 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  10. Niu X., Peng D., Liu F., Liu X.: Lower bounds on the maximum partial correlations of frequency hopping sequence set with low hit zone. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E93-A, 2227–2231 (2010).

  11. Niu X., Peng D., Zhou Z.: New classes of optimal low hit zone frequency hopping sequences with new parameters by interleaving technique. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E95-A, 1835–1842 (2012).

  12. Peng D., Fan P.: 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 

  13. Peng D., Han H.: Frequency/time hopping sequences with no hit zone: bounds and designs. J. Chengdu Univ. Inf. Technol. 30, 1–6 (2015).

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  15. Specification of the Bluetooth Systems-Core. The Bluetooth Special Interest Group (SIG). http://www.bluetooth.com.

  16. Wang X., Fan P.: 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).

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

    Google Scholar 

  18. Ye W., Fan P.: Two classes of frequency hopping sequences with no-hit zone. In: Proceedings of the 7th International Symposium on Communication Theory and Applications, Ambleside, UK, pp. 304–306 (2003).

  19. Zhou Z., Tang X., Udaya P.: New classes of frequency-hopping sequences with optimal partial correlation. IEEE Trans. Inf. Theory 58, 453–458 (2012).

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by National Science Foundation of China (Grant No. 61271244), National High Technology Research and Development Program of China (863 Program) (Grant No. 2015AA01A705), and National Science Foundation of China (Grant No. 61571373).

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Authors and Affiliations

  1. Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University, Chengdu, China

    Limengnan Zhou, Daiyuan Peng, Changyuan Wang & Zheng Ma

  2. School of Transportation and Logistics, Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University, Chengdu, China

    Hongbin Liang

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  1. Limengnan Zhou
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  2. Daiyuan Peng
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  3. Hongbin Liang
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  4. Changyuan Wang
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  5. Zheng Ma
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Corresponding author

Correspondence to Hongbin Liang.

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Communicated by C. Mitchell.

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Zhou, L., Peng, D., Liang, H. et al. Constructions of optimal low-hit-zone frequency hopping sequence sets. Des. Codes Cryptogr. 85, 219–232 (2017). https://doi.org/10.1007/s10623-016-0299-z

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  • DOI: https://doi.org/10.1007/s10623-016-0299-z

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