TY - JOUR
T1 - Two-Dimensional Binary Z-Complementary Array Pairs
AU - Pai, Cheng Yu
AU - Ni, Yong Ting
AU - Chen, Chao Yu
N1 - Funding Information:
Manuscript received October 20, 2019; revised August 27, 2020; accepted January 5, 2021. Date of publication January 19, 2021; date of current version May 20, 2021. This work was supported in part by the Ministry of Science and Technology, Taiwan, under Grant MOST 107-2221-E-006-065-MY2 and Grant MOST 109-2628-E-006-008-MY3. This article was presented in part at the 2019 IEEE International Symposium on Information Theory (ISIT). (Corresponding author: Chao-Yu Chen.) The authors are with the Department of Engineering Science, National Cheng Kung University, Tainan 701, Taiwan (e-mail: [email protected]; [email protected]; super@mail. ncku.edu.tw). Communicated by S. Mesnager, Associate Editor for Sequences.
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2021/6
Y1 - 2021/6
N2 - One-dimensional (1-D) Golay complementary pair (GCP) and its extension Z-complementary pair (ZCP) with additional zero autocorrelation zone property have been widely studied in the literature. Recently, the investigation of 1-D GCPs have been extended to two-dimensional (2-D) and higher dimensional Golay complementary array pairs (GCAPs). In this article, the concept of zero correlation zone (ZCZ) is applied to 2-D GCAP and the 2-D Z-complementary array pair (ZCAP) is presented. Several constructions of ZCAPs are proposed in this article and the existence of ZCAPs is discussed as well. Based on the proposed constructions, 2-D ZCAPs are shown to exist for all sizes. Furthermore, an upper bound on the rectangular ZCZ size of the 2-D ZCAP is derived when both dimensions are odd. The proposed constructions can include ZCAPs which achieve the upper bound.
AB - One-dimensional (1-D) Golay complementary pair (GCP) and its extension Z-complementary pair (ZCP) with additional zero autocorrelation zone property have been widely studied in the literature. Recently, the investigation of 1-D GCPs have been extended to two-dimensional (2-D) and higher dimensional Golay complementary array pairs (GCAPs). In this article, the concept of zero correlation zone (ZCZ) is applied to 2-D GCAP and the 2-D Z-complementary array pair (ZCAP) is presented. Several constructions of ZCAPs are proposed in this article and the existence of ZCAPs is discussed as well. Based on the proposed constructions, 2-D ZCAPs are shown to exist for all sizes. Furthermore, an upper bound on the rectangular ZCZ size of the 2-D ZCAP is derived when both dimensions are odd. The proposed constructions can include ZCAPs which achieve the upper bound.
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U2 - 10.1109/TIT.2021.3052920
DO - 10.1109/TIT.2021.3052920
M3 - Article
AN - SCOPUS:85099733014
SN - 0018-9448
VL - 67
SP - 3892
EP - 3904
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 6
M1 - 9328523
ER -