February  2015, 9(1): 9-21. doi: 10.3934/amc.2015.9.9

Zero correlation zone sequence set with inter-group orthogonal and inter-subgroup complementary properties

1. 

College of Communication Engineering, Chongqing University, Chongqing 400044, China, China

2. 

College of Communication Engineering, Chongqing University, Chongqing 400044, China, and Chongqing Key Laboratory of Emergency Communication, Chongqing Communication Institute, Chongqing 400035

3. 

Chongqing Key Laboratory of Emergency Communication, Chongqing Communication Institute, Chongqing 400035

Received  August 2013 Published  February 2015

In this paper, a novel method for constructing complementary sequence set with zero correlation zone (ZCZ) is presented by interleaving and combining three orthogonal matrices. The constructed set can be divided into multiple sequence groups and each sequence group can be further divided into multiple sequence subgroups. In addition to ZCZ properties of sequences from the same sequence subgroup, sequences from different sequence groups are orthogonal to each other while sequences from different sequence subgroups within the same sequence group possess ideal cross-correlation properties, that is, the proposed ZCZ sequence set has inter-group orthogonal (IGO) and inter-subgroup complementary (ISC) properties. Compared with previous methods, the new construction can provide flexible choice for ZCZ width and set size, and the resultant sequences which are called IGO-ISC sequences in this paper can achieve the theoretical bound on the set size for the ZCZ width and sequence length.
Citation: Zhenyu Zhang, Lijia Ge, Fanxin Zeng, Guixin Xuan. Zero correlation zone sequence set with inter-group orthogonal and inter-subgroup complementary properties. Advances in Mathematics of Communications, 2015, 9 (1) : 9-21. doi: 10.3934/amc.2015.9.9
References:
[1]

H. H. Chen, Y. C. Yeh, et al., Generalized pairwise complementary codes with set-wise uniform interference-free windows,, IEEE J. Sel. Areas Commun., 24 (2006), 65.   Google Scholar

[2]

P. Z. Fan, N. Suehiro, N. Kuroyanagi and X. M. Deng, A class of binary sequences with zero correlation zone,, Electr. Lett., 35 (1999), 777.   Google Scholar

[3]

P. Z. Fan, W. N. Yuan and Y. F. Tu, Z-complementary binary sequences,, IEEE Signal Process. Lett., 14 (2007), 509.   Google Scholar

[4]

L. F. Feng, P. Z. Fan, X. H. Tang and K.-K. Loo, Generalized pairwise Z-complementary codes,, IEEE Signal Process. Lett., 15 (2008), 377.   Google Scholar

[5]

L. F. Feng, X. W. Zhou and P. Z. Fan, A construction of inter-group complementary codes with flexible ZCZ length,, J. Zhejiang Univ. Sci. C, 12 (2011), 846.   Google Scholar

[6]

L. F. Feng, X. W. Zhou and X. Y. Li, A general construction of inter-group complementary codes based on Z-complementary codes and perfect periodic cross-correlation codes,, Wireless Pers. Commun., 71 (2012), 695.   Google Scholar

[7]

M. J. E. Golay, Complementary series,, IRE. Trans. Inf. Theory, 7 (1961), 82.   Google Scholar

[8]

T. Hayashi, Ternary sequence set having periodic and aperiodic zero-correlation zone,, IEICE Trans. Fundamentals, E89-A (2006), 1825.   Google Scholar

[9]

T. Hayashi, T. Maeda and S. Matsufuji, A generalized construction scheme of a zero-correlation zone sequence set with a wide inter-subset zero-correlation zone,, IEICE Trans. Fundamentals, E95-A (2012), 1931.   Google Scholar

[10]

T. Hayashi, T. Maeda, S. Matsufuji and S. Okawa, A ternary zero-correlation zone sequence set having wide inter-subset zero-correlation zone,, IEICE Trans. Fundamentals, E94-A (2011), 2230.   Google Scholar

[11]

T. Hayashi, T. Maeda and S. Okawa, A generalized construction of zero-correlation zone sequence set with sequence subsets,, IEICE Trans. Fundamentals, E94-A (2011), 1597.   Google Scholar

[12]

T. Hayashi and S. Matsufuji, A generalized construction of optimal zero-correlation zone sequence set from a perfect sequence pair,, IEICE Trans. Fundamentals, E93-A (2010), 2337.   Google Scholar

[13]

H. G. Hu and G. Gong, New sets of zero or low correlation zone sequences via interleaving techniques,, IEEE Trans. Inf. Theory, 56 (2010), 1702.  doi: 10.1109/TIT.2010.2040887.  Google Scholar

[14]

J. W. Jang, Y. S. Kim and S. H. Kim, New design of quaternary LCZ and ZCZ sequence set from binary LCZ and ZCZ sequence set,, Adv. Math. Commun., 3 (2009), 115.  doi: 10.3934/amc.2009.3.115.  Google Scholar

[15]

J. W. Jang, Y. S. Kim, S. H. Kim and D. W. Lim, New construction methods of quaternary periodic complementary sequence sets,, Adv. Math. Commun., 4 (2010), 61.  doi: 10.3934/amc.2010.4.61.  Google Scholar

[16]

J. Li, A. P. Huang, M. Guizani and H. H. Chen, Inter-group complementary codes for interference-resistant CDMA wireless communications,, IEEE Trans. Wireless Commun., 7 (2008), 166.   Google Scholar

[17]

X. D. Li, P. Z. Fan, X. H. Tang and L. Hao, Quadriphase Z-complementary sequences,, IEICE Trans. Fundamentals, E93-A (2010), 2251.   Google Scholar

[18]

Y. B. Li, C. Q. Xu and K. Liu, Construction of mutually orthogonal zero correlation zone polyphase sequence sets,, IEICE Trans. Fundamentals, E94-A (2011), 1159.   Google Scholar

[19]

S. Matsufuji, T. Matsumoto, T. Hayashida, T. Hayashi, N. Kuroyanagi and P. Z. FAN, On a ZCZ code including a sequence used for a synchronization symbol,, IEICE Trans. Fundamentals, E93-A (2010), 2286.   Google Scholar

[20]

K. Omata, H. Torii and T. Matsumoto, Zero-cross-correlation properties of asymmetric ZCZ sequence sets,, IEICE Trans. Fundamentals, E95-A (2012), 1926.   Google Scholar

[21]

A. Rathinakumar and A. K. Chaturvedi, Mutually orthogonal sets of ZCZ sequences,, Electron. Lett., 40 (2004), 1133.   Google Scholar

[22]

A. Rathinakumar and A. K. Chaturvedi, A new framework for constructing mutually orthogonal complementary sets and ZCZ sequences,, IEEE Trans. Inf. Theory, 52 (2006), 3817.  doi: 10.1109/TIT.2006.878171.  Google Scholar

[23]

A. Rathinakumar and A. K. Chaturvedi, Complete mutually orthogonal Golay complementary sets from Reed-Muller codes,, IEEE Trans. Inf. Theory, 54 (2008), 1339.  doi: 10.1109/TIT.2007.915980.  Google Scholar

[24]

X. H. Tang, P. Z. Fan and J. Lindner, Multiple binary ZCZ sequence sets with good cross-correlation property based on complementary sequence sets,, IEEE Trans. Inf. Theory, 56 (2010), 4038.  doi: 10.1109/TIT.2010.2050796.  Google Scholar

[25]

X. H. Tang and W. H. Mow, Design of spreading codes for quasi-synchronous CDMA with intercell interference,, IEEE J. Sel. Areas Commun., 24 (2006), 84.   Google Scholar

[26]

X. H. Tang and W. H. Mow, A new systematic construction of zero correlation zone sequences based on interleaved perfect sequences,, IEEE Trans. Inf. Theory, 54 (2008), 5729.  doi: 10.1109/TIT.2008.2006574.  Google Scholar

[27]

H. Torii, T. Matsumoto and M. Nakamura, A new method for constructing asymmetric ZCZ sequences sets,, IEICE Trans. Fundamentals, E95-A (2012), 1577.   Google Scholar

[28]

H. Torii, M. Nakamura and N. Suehiro, A new class of zero-correlation zone sequences,, IEEE Trans. Inf. Theory, 50 (2004), 559.  doi: 10.1109/TIT.2004.825399.  Google Scholar

[29]

H. Torii, M. Satoh, T. Matsumoto and M. Nakamura, Generalized mutually orthogonal ZCZ sequence sets based on perfect sequences and orthogonal codes,, in Proc. 15th Int. Conf. Adv. Commun. Techn., (2013), 894.   Google Scholar

[30]

H. Torii, M. Satoh, T. Matsumoto and M. Nakamura, Quasi-optimal and optimal generalized mutually orthogonal ZCZ sequence sets based on an interleaving technique,, Int. J. Commun., 7 (2013), 18.   Google Scholar

[31]

Y. F. Tu, P. Z. Fan, L. Hao and X. Y. Li, Construction of binary array set with zero correlation zone based on interleaving technique,, IEICE Trans. Fundamentals, E94-A (2011), 766.  doi: 10.1587/transfun.E94.A.766.  Google Scholar

[32]

Y. F. Tu, P. Z. Fan, L. Hao and X. H. Tang, A simple method for generating optimal Z-periodic complementary sequence set based on phase shift,, IEEE Signal Process. Lett., 17 (2010), 891.   Google Scholar

[33]

F. X. Zeng, New perfect ployphase sequences and mutually orthogonal ZCZ polyphase sequence sets,, IEICE trans. Fundamentals, E92-A (2009), 1731.   Google Scholar

[34]

F. X. Zeng, X. P. Zeng, Z. Y. Zhang and G. X. Xuan, Quaternary periodic complementary/Z-complementary sequence sets based upon interleaving technique and Gray mapping,, Adv. Math. Commun., 6 (2012), 237.  doi: 10.3934/amc.2012.6.237.  Google Scholar

[35]

C. Zhang, X. M. Tao, S. Yamada and M. Hatori, Sequence set with three zero correlation zone and its application in MC-CDMA system,, IEICE Trans. Fundamentals, E89-A (2006), 2275.  doi: 10.1093/ietfec/e89-a.9.2275.  Google Scholar

[36]

Z. Y. Zhang, W. Chen, F. X. Zeng, H. Wu and Y. H. Zhong, Z-complementary sets based on sequences with periodic and aperiodic zero correlation zone,, EURASIP J. Wireless Comm. Networking, 2009 (2009), 1.  doi: 10.1155/2009/418026.  Google Scholar

[37]

Z. Y. Zhang, F. X. Zeng and G. X. Xuan, A class of complementary sequences with multi-width zero cross-correlation zone,, IEICE Trans. Fundamentals, E93-A (2010), 1508.  doi: 10.1587/transfun.E93.A.1508.  Google Scholar

[38]

Z. C. Zhou, X. H. Tang and G. Gong, A new class of sequences with zero or low correlation zone based on interleaving technique,, IEEE Trans. Inf. Theory, 54 (2008), 4267.  doi: 10.1109/TIT.2008.928256.  Google Scholar

show all references

References:
[1]

H. H. Chen, Y. C. Yeh, et al., Generalized pairwise complementary codes with set-wise uniform interference-free windows,, IEEE J. Sel. Areas Commun., 24 (2006), 65.   Google Scholar

[2]

P. Z. Fan, N. Suehiro, N. Kuroyanagi and X. M. Deng, A class of binary sequences with zero correlation zone,, Electr. Lett., 35 (1999), 777.   Google Scholar

[3]

P. Z. Fan, W. N. Yuan and Y. F. Tu, Z-complementary binary sequences,, IEEE Signal Process. Lett., 14 (2007), 509.   Google Scholar

[4]

L. F. Feng, P. Z. Fan, X. H. Tang and K.-K. Loo, Generalized pairwise Z-complementary codes,, IEEE Signal Process. Lett., 15 (2008), 377.   Google Scholar

[5]

L. F. Feng, X. W. Zhou and P. Z. Fan, A construction of inter-group complementary codes with flexible ZCZ length,, J. Zhejiang Univ. Sci. C, 12 (2011), 846.   Google Scholar

[6]

L. F. Feng, X. W. Zhou and X. Y. Li, A general construction of inter-group complementary codes based on Z-complementary codes and perfect periodic cross-correlation codes,, Wireless Pers. Commun., 71 (2012), 695.   Google Scholar

[7]

M. J. E. Golay, Complementary series,, IRE. Trans. Inf. Theory, 7 (1961), 82.   Google Scholar

[8]

T. Hayashi, Ternary sequence set having periodic and aperiodic zero-correlation zone,, IEICE Trans. Fundamentals, E89-A (2006), 1825.   Google Scholar

[9]

T. Hayashi, T. Maeda and S. Matsufuji, A generalized construction scheme of a zero-correlation zone sequence set with a wide inter-subset zero-correlation zone,, IEICE Trans. Fundamentals, E95-A (2012), 1931.   Google Scholar

[10]

T. Hayashi, T. Maeda, S. Matsufuji and S. Okawa, A ternary zero-correlation zone sequence set having wide inter-subset zero-correlation zone,, IEICE Trans. Fundamentals, E94-A (2011), 2230.   Google Scholar

[11]

T. Hayashi, T. Maeda and S. Okawa, A generalized construction of zero-correlation zone sequence set with sequence subsets,, IEICE Trans. Fundamentals, E94-A (2011), 1597.   Google Scholar

[12]

T. Hayashi and S. Matsufuji, A generalized construction of optimal zero-correlation zone sequence set from a perfect sequence pair,, IEICE Trans. Fundamentals, E93-A (2010), 2337.   Google Scholar

[13]

H. G. Hu and G. Gong, New sets of zero or low correlation zone sequences via interleaving techniques,, IEEE Trans. Inf. Theory, 56 (2010), 1702.  doi: 10.1109/TIT.2010.2040887.  Google Scholar

[14]

J. W. Jang, Y. S. Kim and S. H. Kim, New design of quaternary LCZ and ZCZ sequence set from binary LCZ and ZCZ sequence set,, Adv. Math. Commun., 3 (2009), 115.  doi: 10.3934/amc.2009.3.115.  Google Scholar

[15]

J. W. Jang, Y. S. Kim, S. H. Kim and D. W. Lim, New construction methods of quaternary periodic complementary sequence sets,, Adv. Math. Commun., 4 (2010), 61.  doi: 10.3934/amc.2010.4.61.  Google Scholar

[16]

J. Li, A. P. Huang, M. Guizani and H. H. Chen, Inter-group complementary codes for interference-resistant CDMA wireless communications,, IEEE Trans. Wireless Commun., 7 (2008), 166.   Google Scholar

[17]

X. D. Li, P. Z. Fan, X. H. Tang and L. Hao, Quadriphase Z-complementary sequences,, IEICE Trans. Fundamentals, E93-A (2010), 2251.   Google Scholar

[18]

Y. B. Li, C. Q. Xu and K. Liu, Construction of mutually orthogonal zero correlation zone polyphase sequence sets,, IEICE Trans. Fundamentals, E94-A (2011), 1159.   Google Scholar

[19]

S. Matsufuji, T. Matsumoto, T. Hayashida, T. Hayashi, N. Kuroyanagi and P. Z. FAN, On a ZCZ code including a sequence used for a synchronization symbol,, IEICE Trans. Fundamentals, E93-A (2010), 2286.   Google Scholar

[20]

K. Omata, H. Torii and T. Matsumoto, Zero-cross-correlation properties of asymmetric ZCZ sequence sets,, IEICE Trans. Fundamentals, E95-A (2012), 1926.   Google Scholar

[21]

A. Rathinakumar and A. K. Chaturvedi, Mutually orthogonal sets of ZCZ sequences,, Electron. Lett., 40 (2004), 1133.   Google Scholar

[22]

A. Rathinakumar and A. K. Chaturvedi, A new framework for constructing mutually orthogonal complementary sets and ZCZ sequences,, IEEE Trans. Inf. Theory, 52 (2006), 3817.  doi: 10.1109/TIT.2006.878171.  Google Scholar

[23]

A. Rathinakumar and A. K. Chaturvedi, Complete mutually orthogonal Golay complementary sets from Reed-Muller codes,, IEEE Trans. Inf. Theory, 54 (2008), 1339.  doi: 10.1109/TIT.2007.915980.  Google Scholar

[24]

X. H. Tang, P. Z. Fan and J. Lindner, Multiple binary ZCZ sequence sets with good cross-correlation property based on complementary sequence sets,, IEEE Trans. Inf. Theory, 56 (2010), 4038.  doi: 10.1109/TIT.2010.2050796.  Google Scholar

[25]

X. H. Tang and W. H. Mow, Design of spreading codes for quasi-synchronous CDMA with intercell interference,, IEEE J. Sel. Areas Commun., 24 (2006), 84.   Google Scholar

[26]

X. H. Tang and W. H. Mow, A new systematic construction of zero correlation zone sequences based on interleaved perfect sequences,, IEEE Trans. Inf. Theory, 54 (2008), 5729.  doi: 10.1109/TIT.2008.2006574.  Google Scholar

[27]

H. Torii, T. Matsumoto and M. Nakamura, A new method for constructing asymmetric ZCZ sequences sets,, IEICE Trans. Fundamentals, E95-A (2012), 1577.   Google Scholar

[28]

H. Torii, M. Nakamura and N. Suehiro, A new class of zero-correlation zone sequences,, IEEE Trans. Inf. Theory, 50 (2004), 559.  doi: 10.1109/TIT.2004.825399.  Google Scholar

[29]

H. Torii, M. Satoh, T. Matsumoto and M. Nakamura, Generalized mutually orthogonal ZCZ sequence sets based on perfect sequences and orthogonal codes,, in Proc. 15th Int. Conf. Adv. Commun. Techn., (2013), 894.   Google Scholar

[30]

H. Torii, M. Satoh, T. Matsumoto and M. Nakamura, Quasi-optimal and optimal generalized mutually orthogonal ZCZ sequence sets based on an interleaving technique,, Int. J. Commun., 7 (2013), 18.   Google Scholar

[31]

Y. F. Tu, P. Z. Fan, L. Hao and X. Y. Li, Construction of binary array set with zero correlation zone based on interleaving technique,, IEICE Trans. Fundamentals, E94-A (2011), 766.  doi: 10.1587/transfun.E94.A.766.  Google Scholar

[32]

Y. F. Tu, P. Z. Fan, L. Hao and X. H. Tang, A simple method for generating optimal Z-periodic complementary sequence set based on phase shift,, IEEE Signal Process. Lett., 17 (2010), 891.   Google Scholar

[33]

F. X. Zeng, New perfect ployphase sequences and mutually orthogonal ZCZ polyphase sequence sets,, IEICE trans. Fundamentals, E92-A (2009), 1731.   Google Scholar

[34]

F. X. Zeng, X. P. Zeng, Z. Y. Zhang and G. X. Xuan, Quaternary periodic complementary/Z-complementary sequence sets based upon interleaving technique and Gray mapping,, Adv. Math. Commun., 6 (2012), 237.  doi: 10.3934/amc.2012.6.237.  Google Scholar

[35]

C. Zhang, X. M. Tao, S. Yamada and M. Hatori, Sequence set with three zero correlation zone and its application in MC-CDMA system,, IEICE Trans. Fundamentals, E89-A (2006), 2275.  doi: 10.1093/ietfec/e89-a.9.2275.  Google Scholar

[36]

Z. Y. Zhang, W. Chen, F. X. Zeng, H. Wu and Y. H. Zhong, Z-complementary sets based on sequences with periodic and aperiodic zero correlation zone,, EURASIP J. Wireless Comm. Networking, 2009 (2009), 1.  doi: 10.1155/2009/418026.  Google Scholar

[37]

Z. Y. Zhang, F. X. Zeng and G. X. Xuan, A class of complementary sequences with multi-width zero cross-correlation zone,, IEICE Trans. Fundamentals, E93-A (2010), 1508.  doi: 10.1587/transfun.E93.A.1508.  Google Scholar

[38]

Z. C. Zhou, X. H. Tang and G. Gong, A new class of sequences with zero or low correlation zone based on interleaving technique,, IEEE Trans. Inf. Theory, 54 (2008), 4267.  doi: 10.1109/TIT.2008.928256.  Google Scholar

[1]

Thierry Horsin, Mohamed Ali Jendoubi. On the convergence to equilibria of a sequence defined by an implicit scheme. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020465

[2]

Yuanfen Xiao. Mean Li-Yorke chaotic set along polynomial sequence with full Hausdorff dimension for $ \beta $-transformation. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 525-536. doi: 10.3934/dcds.2020267

[3]

Xinpeng Wang, Bingo Wing-Kuen Ling, Wei-Chao Kuang, Zhijing Yang. Orthogonal intrinsic mode functions via optimization approach. Journal of Industrial & Management Optimization, 2021, 17 (1) : 51-66. doi: 10.3934/jimo.2019098

[4]

Laurent Di Menza, Virginie Joanne-Fabre. An age group model for the study of a population of trees. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020464

[5]

Qiao Liu. Local rigidity of certain solvable group actions on tori. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 553-567. doi: 10.3934/dcds.2020269

[6]

Kien Trung Nguyen, Vo Nguyen Minh Hieu, Van Huy Pham. Inverse group 1-median problem on trees. Journal of Industrial & Management Optimization, 2021, 17 (1) : 221-232. doi: 10.3934/jimo.2019108

[7]

Youshan Tao, Michael Winkler. Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 439-454. doi: 10.3934/dcds.2020216

2019 Impact Factor: 0.734

Metrics

  • PDF downloads (175)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]