Skip to main content
Erschienen in: Designs, Codes and Cryptography 2/2014

01.08.2014

New sets of frequency-hopping sequences with optimal Hamming correlation

verfasst von: Wenli Ren, Fang-Wei Fu, Zhengchun Zhou

Erschienen in: Designs, Codes and Cryptography | Ausgabe 2/2014

Einloggen, um Zugang zu erhalten

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Frequency-hopping spread spectrum and direct-sequence spread spectrum are two main spread coding technologies in communication systems. Frequency-hopping sequences are needed in FH-CDMA systems. In this paper, a construction of optimal sets of frequency-hopping sequences using cyclotomy and the Chinese remainder theorem is introduced. It generalizes some earlier constructions, and produces new optimal sets of frequency-hopping sequences.
Literatur
1.
Zurück zum Zitat Cao, Z., Ge, G., Miao, Y.: Combinatorial characterizations of one-coincidence frequency-hopping sequences. Des. Codes Cryptogr. 41, 177–184 (2006)CrossRefMATHMathSciNet Cao, Z., Ge, G., Miao, Y.: Combinatorial characterizations of one-coincidence frequency-hopping sequences. Des. Codes Cryptogr. 41, 177–184 (2006)CrossRefMATHMathSciNet
2.
Zurück zum Zitat Chu, W., Colbourn, C.J.: Optimal frequency-hopping sequences via cyclotomy. IEEE Trans. Inf. Theory 51, 1139–1141 (2005)CrossRefMathSciNet Chu, W., Colbourn, C.J.: Optimal frequency-hopping sequences via cyclotomy. IEEE Trans. Inf. Theory 51, 1139–1141 (2005)CrossRefMathSciNet
3.
Zurück zum Zitat Chung, J.H., Han, Y.K., Yang, K.: New classes of optimal frequency-hopping sequences by interleaving techniques. IEEE Trans. Inf. Theory 55, 5783–5791 (2009)CrossRefMathSciNet Chung, J.H., Han, Y.K., Yang, K.: New classes of optimal frequency-hopping sequences by interleaving techniques. IEEE Trans. Inf. Theory 55, 5783–5791 (2009)CrossRefMathSciNet
4.
Zurück zum Zitat Ding, C.S., Moisio, M.J., Yuan, J.: Algebraic constrctions of optimal frequency-hopping sequences. IEEE Trans. Inf. Theory 53, 2606–2610 (2007)CrossRefMATHMathSciNet Ding, C.S., Moisio, M.J., Yuan, J.: Algebraic constrctions of optimal frequency-hopping sequences. IEEE Trans. Inf. Theory 53, 2606–2610 (2007)CrossRefMATHMathSciNet
5.
Zurück zum Zitat Ding, C.S., Yin, J.: IEEE Trans. Inf. Theory. Sets of optimal frequency-hopping sequences 54, 3741–3745 (2008)MathSciNet Ding, C.S., Yin, J.: IEEE Trans. Inf. Theory. Sets of optimal frequency-hopping sequences 54, 3741–3745 (2008)MathSciNet
6.
Zurück zum Zitat Ding, C.S., Fuji-Hara, Y., Fujiwara, Y., Jinbo, M., Mishima, M.: Sets of optimal frequency-hopping sequences: bounds and optimal constrctions. IEEE Trans. Inf. Theory 55, 3797–3804 (2009) Ding, C.S., Fuji-Hara, Y., Fujiwara, Y., Jinbo, M., Mishima, M.: Sets of optimal frequency-hopping sequences: bounds and optimal constrctions. IEEE Trans. Inf. Theory 55, 3797–3804 (2009)
7.
Zurück zum Zitat Fuji-Hara, R., Miao, Y., Mishima, M.: Optimal frequency-hopping sequences: a combinatorial approach. IEEE Trans. Inf. Theory 50, 2408–2420 (2004)CrossRefMathSciNet Fuji-Hara, R., Miao, Y., Mishima, M.: Optimal frequency-hopping sequences: a combinatorial approach. IEEE Trans. Inf. Theory 50, 2408–2420 (2004)CrossRefMathSciNet
8.
Zurück zum Zitat Ge, G.N., Fuji-Hara, R.F., Miao, Y.: Further combinatorial constrcutions for optimal frequency-hopping sequences. J. Comb. Theory Ser. A 113, 1699–1718 (2006)CrossRefMATHMathSciNet Ge, G.N., Fuji-Hara, R.F., Miao, Y.: Further combinatorial constrcutions for optimal frequency-hopping sequences. J. Comb. Theory Ser. A 113, 1699–1718 (2006)CrossRefMATHMathSciNet
9.
Zurück zum Zitat Ge, G.N., Miao, Y., Yao, Z.: Optimal frequency-hopping sequences: auto and cross corelation properties. IEEE Trans. Inf. Theory 55, 867–879 (2009)CrossRefMathSciNet Ge, G.N., Miao, Y., Yao, Z.: Optimal frequency-hopping sequences: auto and cross corelation properties. IEEE Trans. Inf. Theory 55, 867–879 (2009)CrossRefMathSciNet
10.
Zurück zum Zitat Han, Y.K., Yang, K.: On the Sidel’nikov sequences as frequency-hopping sequences. IEEE Trans. Inf. Theory 55, 4279–4285 (2009)CrossRefMathSciNet Han, Y.K., Yang, K.: On the Sidel’nikov sequences as frequency-hopping sequences. IEEE Trans. Inf. Theory 55, 4279–4285 (2009)CrossRefMathSciNet
11.
Zurück zum Zitat Lempel, A., Greenberger, H.: Families of sequences with optimal Hamming correlation properties. IEEE Trans. Inf. Theory 20, 90–94 (1974)CrossRefMATHMathSciNet Lempel, A., Greenberger, H.: Families of sequences with optimal Hamming correlation properties. IEEE Trans. Inf. Theory 20, 90–94 (1974)CrossRefMATHMathSciNet
12.
Zurück zum Zitat Liu, F., Peng, D.Y., Zhou, Z.C., Tang, X.H.: A new frequency-hopping sequence set based upon generalized cyclotomy. Des. Codes and Cryptogr. (2012, in press) Liu, F., Peng, D.Y., Zhou, Z.C., Tang, X.H.: A new frequency-hopping sequence set based upon generalized cyclotomy. Des. Codes and Cryptogr. (2012, in press)
13.
Zurück zum Zitat Peng, D.Y., Fan, P.Z.: Low bounds on the Hamming auto and cross-correlation of frequency-hopping sequences. IEEE Trans. Inf. Theory 50, 2149–2154 (2004)CrossRefMathSciNet Peng, D.Y., Fan, P.Z.: Low bounds on the Hamming auto and cross-correlation of frequency-hopping sequences. IEEE Trans. Inf. Theory 50, 2149–2154 (2004)CrossRefMathSciNet
15.
Zurück zum Zitat Storer, T.: Cyclotomy and differrence sets. Markam, Chicago (1967) Storer, T.: Cyclotomy and differrence sets. Markam, Chicago (1967)
16.
Zurück zum Zitat Zhang Y., Ke P.H., Zhang S.Y.: Optimal frequency-hopping sequences based on cyclotomy. In: First International Workshop on Education Technology and Computer Science, vol. 1, pp. 1122–1126. (2009) Zhang Y., Ke P.H., Zhang S.Y.: Optimal frequency-hopping sequences based on cyclotomy. In: First International Workshop on Education Technology and Computer Science, vol. 1, pp. 1122–1126. (2009)
17.
Zurück zum Zitat 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)CrossRefMathSciNet 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)CrossRefMathSciNet
18.
Zurück zum Zitat 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)CrossRefMathSciNet 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)CrossRefMathSciNet
Metadaten
Titel
New sets of frequency-hopping sequences with optimal Hamming correlation
verfasst von
Wenli Ren
Fang-Wei Fu
Zhengchun Zhou
Publikationsdatum
01.08.2014
Verlag
Springer US
Erschienen in
Designs, Codes and Cryptography / Ausgabe 2/2014
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-012-9774-3

Weitere Artikel der Ausgabe 2/2014

Designs, Codes and Cryptography 2/2014 Zur Ausgabe