Lower Bounds on Correlation of Z-Complementary Code Sets

Authors:
Lifang Feng;Pingzhi Fan;Xianwei Zhou
Affiliations:
School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing, China 100083;Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University, Chengdu, China 610031;School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing, China 100083
Venue:
Wireless Personal Communications: An International Journal
Year:
2013

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Abstract

A set of binary codes is called a Z-complementary code set if the sum of the autocorrelation functions of the codes involved is zero in the zero correlation zone (ZCZ) except at zero shift. Comparing to the traditional complementary code sets, the Z-complementary code sets not only have more freedom on the code length, but also have much more mates. In this paper, lower bounds on periodic/aperiodic correlation of Z-complementary binary code sets with respect to the number of mates, family size, sequence length, the length of ZCZ, maximum periodic/aperiodic autocorrelation sidelobe inside the ZCZ and maximum periodic/aperiodic crosscorrelation value inside the ZCZ, are derived. The proposed lower bounds provide theoretical criteria for designing, optimizing and choosing Z-complementary code set in applications.