Quaternary periodic complementary/Z-complementary sequence sets based on interleaving technique and Gray mapping

Fanxin Zeng; Xiaoping Zeng; Zhenyu Zhang; Guixin Xuan

doi:10.3934/amc.2012.6.237

Article Contents

2012, Volume 6, Issue 2: 237-247. Doi: 10.3934/amc.2012.6.237

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Quaternary periodic complementary/Z-complementary sequence sets based on interleaving technique and Gray mapping

1.
College of Communication Engineering, Chongqing University, Chongqing 400044, China, and Chongqing Key Laboratory of Emergency Communication, Chongqing Communication Institute, Chongqing 400035
2.
College of Communication Engineering, Chongqing University, Chongqing 400044
3.
Chongqing Key Laboratory of Emergency Communication, Chongqing Communication Institute, Chongqing 400035

Received: May 31, 2011

Revised: December 31, 2011

Published: April 2012

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Abstract

A family of quaternary periodic complementary sequence (PCS) or Z-complementary sequence (PZCS) sets is presented. By combining an interleaving technique and the inverse Gray mapping, the proposed method transforms the known binary PCS/PZCS sets with odd length of sub-sequences into quaternary PCS/PZCS sets, but the length of new sub-sequences is twice as long as that of the original sub-sequences, which is a drawback of this proposed method. However, the shortcoming that the method proposed by J. W. Jang, et al. is merely fit for even length of sub-sequences is overcome. As a consequence, the union of our and J. W. Jang, et al.'s methods allows us to construct quaternary PCS/PZCS sets from binary PCS/PZCS sets with sub-sequences of arbitrary length.

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Mathematics Subject Classification: Primary: 11B50, 94A55; Secondary: 11B75.

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