Abstract
In quasi-synchronous frequency-hopping multiple-access systems, low-hit-zone frequency-hopping sequence (LHZ-FHS) sets are commonly employed to minimize multiple-access interferences. In this paper, we present (near-)optimal LHZ-FHS sets with new parameters. We first analyze the Hamming correlation of frequency-hopping sequences (FHSs) constructed by the Cartesian product. We then present a new optimal LHZ-FHS set with respect to the Peng-Fan-Lee bound, which is obtained from the Cartesian product of two one-coincidence FHS sets. We also construct a near-optimal LHZ-FHS set from Kumar’s FHS set.
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST) (No. 2012-0005686).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Simon, M.K., Omura, J.K., Scholtz, R.A., Levitt, B.K.: Spread Spectrum Communications Handbook (Revised Ed.). McGraw-Hill Inc. (1994)
Sarwate, D.V.: Reed-Solomon codes and the design of sequences for spread-spectrum multiple-access communications. In: Wicker, S.B., Bharagava, V.K. (eds.) Reed-Solomon Codes and Their Applications. IEEE Press, Piscataway (1994)
Fan, P., Darnell, M.: Sequence Design for Communications Applications. Research Studies Press (RSP), John Wiley & Sons, London, UK (1996)
Lempel, A., Greenberger, H.: Families of sequences with optimal Hamming correlation properties. IEEE Trans. Inform. Theory 20(1), 90–94 (1974)
Kumar, P.V.: Frequency-hopping code sequence designs having large linear span. IEEE Trans. Inform. Theory 34(1), 146–151 (1988)
Udaya, P., Siddiqi, M.U.: Optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings. IEEE Trans. Inform. Theory 44(4), 1492–1503 (1998)
Chu, W., Colbourn, C.J.: Optimal frequency-hopping sequences via cyclotomy. IEEE Trans. Inform. Theory 51(3), 1139–1141 (2005)
Ding, C., Yin, J.: Sets of optimal frequency-hopping sequences. IEEE Trans. Inform. Theory 54(8), 3741–3745 (2008)
Han, Y.K., Yang, K.: On the Sidel’nikov sequences as frequency-hopping sequences. IEEE Trans. Inform. Theory 55(9), 4279–4285 (2009)
Chung, J.-H., Han, Y.K., Yang, K.: New classes of optimal frequency-hopping sequences by interleaving techniques. IEEE Trans. Inform. Theory 55(12), 5783–5791 (2009)
Chung, J.-H., Yang, K.: Optimal frequency-hopping sequences with new parameters. IEEE Trans. Inform. Theory 56(4), 1685–1693 (2010)
Chung, J.-H., Yang, K.: k-fold cyclotomy and its application to frequency-hopping sequences. IEEE Trans. Inform. Theory 57(4), 2306–2317 (2011)
Zhou, Z., Tang, X., Peng, D., Udaya, P.: New constructions for optimal sets of frequency-hopping sequences. IEEE Trans. Inform. Theory 57(6), 3831–3840 (2011)
Ye, W., Fan, P.: Two classes of frequency hopping sequences with no-hit zone. In: Proc. 7th Intl. Symp. Commun. Theory Appl., Ambleside, UK, pp. 304–306 (2003)
Wang, X., Fan, P.: A class of frequency hopping sequences with no hit zone. In: Proc. 4th Intl. Conf. Par. Dist. Comp., Appl. Tech., Chengdu, China, pp. 896–898 (2003)
Ye, W., Fan, P., Gabidulin, E.M.: Construction of non-repeating frequency-hopping sequences with no-hit zone. Electronics Letters 42(8), 681–682 (2006)
Chung, J.-H., Han, Y.K., Yang, K.: No-hit-zone frequency-hopping sequence sets with optimal Hamming autocorrelation. IEICE Trans. Fund. Elec. Commun. Comp. Sci. 93-A(11), 2239–2244 (2010)
Peng, D., Fan, P., Lee, M.H.: Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone. Sci. China Ser. F Inform. Sci. 49(2), 208–218 (2006)
Ma, W., Sun, S.: New designs of frequency hopping sequences with low hit zone. Des. Codes Crypt. 60(2), 145–153 (2011)
Niu, X., Peng, D., Zhou, Z.: New classes of optimal frequency hopping sequences with low hit zone with new parameters. In: The Fifth International Workshop on Signal Design and its Applications in Communications (IWSDA 2011), Guilin, China, October 10-14, pp. 111–114 (2011)
Gong, G.: Theory and applications of q-ary interleaved sequences. IEEE Trans. Inform. Theory 41(2), 400–411 (1995)
Solomon, G.: Optimal frequency hopping for multiple access. In: Proc. 1977 Symp. Spread Spectrum Commun., San Diego, CA, USA, March 13-16, pp. 33–35 (1977)
Peng, D., Fan, P.: Lower bounds on the Hamming auto- and cross correlations of frequency-hopping sequences. IEEE Trans. Inform. Theory 50(9), 2149–2154 (2004)
Reed, I.S., Solomon, G.: Polynomial cods over certain finite fields. SIAM J. App. Math. 6, 300–304 (1960)
Kumar, P.V., Scholtz, R.A., Welch, L.R.: Generalized bent functions and their properties. J. Comb. Theory Ser. A 40, 90–107 (1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chung, JH., Yang, K. (2012). Low-Hit-Zone Frequency-Hopping Sequence Sets with New Parameters. In: Helleseth, T., Jedwab, J. (eds) Sequences and Their Applications – SETA 2012. SETA 2012. Lecture Notes in Computer Science, vol 7280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30615-0_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-30615-0_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30614-3
Online ISBN: 978-3-642-30615-0
eBook Packages: Computer ScienceComputer Science (R0)