N-Shift Cross-Orthogonal Sequences and Complete Complementary Codes

N-shift cross-orthogonal sequences are powerful materials for constructing complete complementary codes. In this paper, we present six theorems concerning general construction and expansion methods with the least upper bounds for N-shift cross-orthogonal sequences and complete complementary codes. Applying the theorems that about construction and expansion method of N-shift cross-orthogonal sequences, many types of N-shift cross orthogonal sequences are constructed systematically. Those include the sequence sets consisting of different lengths and include previous classes as special cases. Based on the generated N-shift cross orthogonal sequences, a complete complementary code are constructed by the theorem of construction method of complete complementary code. The last theorem which is about expansion method of complete complementary code are given for increase the number of sequence sets.

[1]  Naoki Suehiro,et al.  Complete Complementary Sequences of Different Length , 2007, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[2]  N. Suchiro,et al.  A generation method for constructing (N,N,MN/P) complete complementary sequences , 2004, SympoTIC '04. Joint 1st Workshop on Mobile Future & Symposium on Trends In Communications (IEEE Cat. No.04EX877).

[3]  Chenggao Han.  A Generation Method for Constructing Complete Complementary Sequences , 2004 .

[4]  P. Farkas,et al.  Two-dimensional orthogonal complete complementary codes , 2003, SympoTIC'03. Joint 1st Workshop on Mobile Future and Symposium on Trends in Communications.

[5]  Naoki Suehiro,et al.  General construction of periodic complete complementary codes composed of expanded modulatable orthogonal sequences , 2000, Proceedings ISCC 2000. Fifth IEEE Symposium on Computers and Communications.

[6]  Richard J. Turyn,et al.  Ambiguity functions of complementary sequences (Corresp.) , 1963, IEEE Trans. Inf. Theory.

[7]  R. Sivaswamy,et al.  Multiphase Complementary Codes , 1978, IEEE Trans. Inf. Theory.

[8]  Naoki Suehiro,et al.  N-shift cross-orthogonal sequences , 1988, IEEE Trans. Inf. Theory.

[9]  Marcel J. E. Golay,et al.  Complementary series , 1961, IRE Trans. Inf. Theory.

[10]  Mitsutoshi Hatori,et al.  Even-shift orthogonal sequences , 1969, IEEE Trans. Inf. Theory.

[11]  C.-C. TSENG,et al.  Complementary sets of sequences , 1972, IEEE Trans. Inf. Theory.

[12]  Peter Farkas,et al.  New 2D-MC-DS-SS-CDMA Techniques Based on Two-Dimensional Orthogonal Complete Complementary Codes , 2004 .

[13]  Robert L. Frank,et al.  Polyphase complementary codes , 1980, IEEE Trans. Inf. Theory.

[14]  P. Farkas,et al.  Three-dimensional orthogonal complete complementary codes , 2004, SympoTIC '04. Joint 1st Workshop on Mobile Future & Symposium on Trends In Communications (IEEE Cat. No.04EX877).

[15]  Xiaojing Huang,et al.  Scalable complete complementary sets of sequences , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.