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Front. Inform. Technol. Electron. Eng.  2011, Vol. 12 Issue (10): 846-854    DOI: 10.1631/jzus.C1000360
    
A construction of inter-group complementary codes with flexible ZCZ length
Li-fang Feng*,1, Xian-wei Zhou1, Ping-zhi Fan2
1 School of Information Engineering, University of Science and Technology Beijing, Beijing 100083, China 2 Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University, Chengdu 610031, China
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Abstract  A general construction of inter-group complementary (IGC) codes is proposed based on perfect complementary (PC) codes, interleaving operation, and the orthogonal matrix. The correlation properties of the newly constructed IGC codes can be described as follows: (1) the autocorrelation sidelobes of the codes are zeros in the zero correlation zone (ZCZ); (2) the cross-correlation functions (CCFs) between any two different codes of the same group are zeros in the ZCZ; (3) the CCFs between any two codes of different groups are zeros everywhere. The key point of this construction is that the ZCZ length of the generated IGC codes can be chosen flexibly. It is well known that there is a limitation between the ZCZ length and the number of mates; that is, the smaller is the length of ZCZ, the more are the IGC codes that can be generated. Therefore, if we can choose the ZCZ length of the IGC codes flexibly according to the requirement of the system, more users can be accommodated in the system.

Key words： Z-complementary codes      Perfect complementary codes      Zero correlation zone     
Received: 15 October 2010      Published: 08 October 2011
CLC:  TN914.42  
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Li-fang Feng, Xian-wei Zhou, Ping-zhi Fan. A construction of inter-group complementary codes with flexible ZCZ length. Front. Inform. Technol. Electron. Eng., 2011, 12(10): 846-854.

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http://www.zjujournals.com/xueshu/fitee/10.1631/jzus.C1000360     OR     http://www.zjujournals.com/xueshu/fitee/Y2011/V12/I10/846


A construction of inter-group complementary codes with flexible ZCZ length

A general construction of inter-group complementary (IGC) codes is proposed based on perfect complementary (PC) codes, interleaving operation, and the orthogonal matrix. The correlation properties of the newly constructed IGC codes can be described as follows: (1) the autocorrelation sidelobes of the codes are zeros in the zero correlation zone (ZCZ); (2) the cross-correlation functions (CCFs) between any two different codes of the same group are zeros in the ZCZ; (3) the CCFs between any two codes of different groups are zeros everywhere. The key point of this construction is that the ZCZ length of the generated IGC codes can be chosen flexibly. It is well known that there is a limitation between the ZCZ length and the number of mates; that is, the smaller is the length of ZCZ, the more are the IGC codes that can be generated. Therefore, if we can choose the ZCZ length of the IGC codes flexibly according to the requirement of the system, more users can be accommodated in the system.

关键词： Z-complementary codes,  Perfect complementary codes,  Zero correlation zone 
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