A Novel Construction of Z-Complementary Pairs Based on Generalized Boolean Functions

Binary Golay complementary pairs exist for quite limited lengths whereas the binary Z-complementary pairs (ZCPs) are available for more lengths. Therefore, the ZCPs can potentially find more engineering applications. In this letter, we propose a novel construction of binary and nonbinary ( $q$ -ary for even $q$ ) ZCPs based on generalized Boolean functions. Both even- and odd-length ZCPs can be obtained by the proposed construction. Moreover, the sequence length, the width of zero correlation zone (ZCZ), and the constellation size are all very flexible. A family of ZCPs with large ZCZ widths is presented based on our construction where the width of ZCZ is larger than half of the sequence length. This proposed family includes some previous results on binary ZCPs as special cases.

[1]  Ying Li,et al.  More Golay sequences , 2005, IEEE Trans. Inf. Theory.

[2]  Yong Liang Guan,et al.  16-QAM Almost-Complementary Sequences With Low PMEPR , 2016, IEEE Transactions on Communications.

[3]  Yong Liang Guan,et al.  Optimal Odd-Length Binary Z-Complementary Pairs , 2014, IEEE Transactions on Information Theory.

[4]  Kenneth G. Paterson,et al.  Generalized Reed-Muller codes and power control in OFDM modulation , 1998, IEEE Trans. Inf. Theory.

[5]  Costas N. Georghiades,et al.  Complementary sequences for ISI channel estimation , 2001, IEEE Trans. Inf. Theory.

[6]  Pingzhi Fan,et al.  Generalized Pairwise Z-Complementary Codes , 2008, IEEE Signal Processing Letters.

[7]  Peter B. Borwein,et al.  A complete description of Golay pairs for lengths up to 100 , 2003, Math. Comput..

[8]  Pingzhi Fan,et al.  Z-complementary Binary Sequences , 2007, IEEE Signal Processing Letters.

[9]  Matthew G. Parker,et al.  A Framework for the Construction ofGolay Sequences , 2008, IEEE Transactions on Information Theory.

[10]  Pingzhi Fan,et al.  SEQUENCE DESIGN FOR COMMUNICATIONS APPLICATIONS , 1996 .

[11]  Mathias Friese,et al.  Multitone signals with low crest factor , 1997, IEEE Trans. Commun..

[12]  Yong Liang Guan,et al.  On Even-Period Binary Z-Complementary Pairs with Large ZCZs , 2014, IEEE Signal Processing Letters.

[13]  Branislav M. Popovic,et al.  Synthesis of power efficient multitone signals with flat amplitude spectrum , 1991, IEEE Trans. Commun..

[14]  Ying Li.  A Construction of General QAM Golay Complementary Sequences , 2010, IEEE Transactions on Information Theory.

[15]  Chao-Yu Chen.  Complementary Sets of Non-Power-of-Two Length for Peak-to-Average Power Ratio Reduction in OFDM , 2016, IEEE Transactions on Information Theory.

[16]  J. Jedwab,et al.  Peak-to-mean power control in OFDM, Golay complementary sequences and Reed-Muller codes , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

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

[18]  Pingzhi Fan,et al.  Existence of Binary $Z$-Complementary Pairs , 2011, IEEE Signal Processing Letters.

[19]  Ying Li,et al.  New Constructions of General QAM Golay Complementary Sequences , 2013, IEEE Transactions on Information Theory.

[20]  Matthew G. Parker,et al.  Golay complementary array pairs , 2007, Des. Codes Cryptogr..

[21]  J. Jedwab,et al.  A Framework for the Construction of Golay Sequences , 2008 .

[22]  R. van Nee.  OFDM codes for peak-to-average power reduction and error correction , 1996, Proceedings of GLOBECOM'96. 1996 IEEE Global Telecommunications Conference.

[23]  George R. Welti,et al.  Quaternary codes for pulsed radar , 1960, IRE Trans. Inf. Theory.

[24]  Wai Ho Mow,et al.  New construction of Z-complementary pairs , 2016 .