New Classes of Optimal Low-Hit-Zone Frequency-Hopping Sequence Sets by Cartesian Product

In quasi-synchronous frequency-hopping multiple-access systems where relative delays between different users are restricted within a zone around the origin, low-hit-zone frequency-hopping sequences (LHZ-FHSs) are employed as spreading sequences. In this paper, we study LHZ-FHS sets obtained from the Cartesian product of some FHS sets. We first derive an upper bound on the Hamming correlation of FHSs constructed by the Cartesian product. We also give a general method to construct LHZ-FHS sets by the Cartesian product. We then present four new classes of optimal LHZ-FHS sets. The first three classes of sets are obtained from the product of Solomon's FHS sets and Kumar's FHS sets. The last one is constructed by the product of FHS sets based on interleaving techniques. These LHZ-FHS sets have new parameters not covered in the literature.

[1]  Daiyuan Peng,et al.  New Constructions for Optimal Sets of Frequency-Hopping Sequences , 2011, IEEE Transactions on Information Theory.

[2]  Jin-Ho Chung,et al.  Optimal Frequency-Hopping Sequences With New Parameters , 2010, IEEE Transactions on Information Theory.

[3]  Charles J. Colbourn,et al.  Optimal frequency-hopping sequences via cyclotomy , 2005, IEEE Transactions on Information Theory.

[4]  Jin-Ho Chung,et al.  No-Hit-Zone Frequency-Hopping Sequence Sets with Optimal Hamming Autocorrelation , 2010, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[5]  Cunsheng Ding,et al.  Sets of Optimal Frequency-Hopping Sequences , 2008, IEEE Transactions on Information Theory.

[6]  Jin-Ho Chung,et al.  New Classes of Optimal Frequency-Hopping Sequences by Interleaving Techniques , 2009, IEEE Transactions on Information Theory.

[7]  Pingzhi Fan,et al.  Construction of non-repeating frequency-hopping sequences with no-hit zone , 2006 .

[8]  Pingzhi Fan,et al.  A class of frequency hopping sequences with no hit zone , 2003, Proceedings of the Fourth International Conference on Parallel and Distributed Computing, Applications and Technologies.

[9]  Daiyuan Peng,et al.  Lower Bounds on the Hamming Auto- and Cross Correlations of Frequency-Hopping Sequences , 2004, IEEE Trans. Inf. Theory.

[10]  Daiyuan Peng,et al.  New classes of optimal frequency hopping sequences with low hit zone with new parameters , 2011, Proceedings of the Fifth International Workshop on Signal Design and Its Applications in Communications.

[11]  Shaohui Sun,et al.  New designs of frequency hopping sequences with low hit zone , 2011, Des. Codes Cryptogr..

[12]  Zhengchun Zhou,et al.  A New Class of Sequences With Zero or Low Correlation Zone Based on Interleaving Technique , 2008, IEEE Transactions on Information Theory.

[13]  Jin-Ho Chung,et al.  $k$ -Fold Cyclotomy and Its Application to Frequency-Hopping Sequences , 2011, IEEE Transactions on Information Theory.

[14]  Jin-Ho Chung,et al.  Low-Hit-Zone Frequency-Hopping Sequence Sets with New Parameters , 2012, SETA.

[15]  Daiyuan Peng,et al.  Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone , 2006, Science in China Series F: Information Sciences.

[16]  Abraham Lempel,et al.  Families of sequences with optimal Hamming-correlation properties , 1974, IEEE Trans. Inf. Theory.

[17]  Mohammad Umar Siddiqi,et al.  Optimal Large Linear Complexity Frequency Hopping Patterns Derived from Polynomial Residue Class Rings , 1998, IEEE Trans. Inf. Theory.

[18]  Guang Gong,et al.  Theory and applications of q-ary interleaved sequences , 1995, IEEE Trans. Inf. Theory.

[19]  Pingzhi Fan,et al.  SEQUENCE DESIGN FOR COMMUNICATIONS APPLICATIONS , 1996 .

[20]  Kyeongcheol Yang,et al.  On the Sidel'nikov Sequences as Frequency-Hopping Sequences , 2009, IEEE Transactions on Information Theory.

[21]  P. Vijay Kumar,et al.  Frequency-hopping code sequence designs having large linear span , 1988, IEEE Trans. Inf. Theory.