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

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May 2012, 6(2): 237-247. doi: 10.3934/amc.2012.6.237

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

Fanxin Zeng ^1, , Xiaoping Zeng ^2, , Zhenyu Zhang ^3, and Guixin Xuan ^3,

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

Received June 2011 Revised January 2012 Published April 2012

Abstract
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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.

Keywords: quaternary sequence, Complementary sequence set, Z-complementary sequence seta, interleaving technique, odd period..

Mathematics Subject Classification: Primary: 11B50, 94A55; Secondary: 11B7.

Citation: Fanxin Zeng, Xiaoping Zeng, Zhenyu Zhang, Guixin Xuan. Quaternary periodic complementary/Z-complementary sequence sets based on interleaving technique and Gray mapping. Advances in Mathematics of Communications, 2012, 6 (2) : 237-247. doi: 10.3934/amc.2012.6.237

References:

[1]	R. Appuswamy and A. K. Chaturvedi, A new framework for constructing mutually orthogonal complementary sets and ZCZ sequences,, IEEE Trans. Inform. Theory, 52 (2006), 3817. doi: 10.1109/TIT.2006.878171. Google Scholar
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[6]	D. Ž. Đoković, Note on periodic complementary sets of binary sequences,, Des. Codes Cryptogr., 13 (1998), 251. doi: 10.1023/A:1008245823233. Google Scholar
[7]	D. Ž. Đoković, Periodic complementary sets of binary sequences,, Int. Math. Forum, 4 (2009), 717. Google Scholar
[8]	P. Z. Fan and M. Darnell, "Sequence Design for Communications Applictions,'', John Wiley & Sons Inc., (1996). Google Scholar
[9]	P. Z. Fan, W. N. Yuan and Y. F. Tu, Z-complementary binary sequences,, IEEE Signal Proc. Letters, 14 (2007), 509. doi: 10.1109/LSP.2007.891834. Google Scholar
[10]	K. Feng, P. J. S. Shyue and Q. Xiang, On the aperiodic and periodic complementary binary sequences,, IEEE Trans. Inform. Theory, 45 (1999), 296. doi: 10.1109/18.746823. Google Scholar
[11]	R. L. Frank, Polyphase complementary codes,, IEEE Trans. Inform. Theory, IT-26 (1980), 641. doi: 10.1109/TIT.1980.1056272. Google Scholar
[12]	M. J. E. Golay, Complementary series,, IEEE Trans. Inform. Theory, IT-7 (1960), 82. Google Scholar
[13]	S. W. Golomb and G. Gong, "Signal Design for Good Correlation: for Wireless Communications, Cryptography and Radar Applications,'', Cambridge University Press, (2005). doi: 10.1017/CBO9780511546907. Google Scholar
[14]	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
[15]	S. M. Krone and D. V. Sarwate, Quadriphase sequences for spread spectrum multiple-access communication,, IEEE Trans. Inform. Theory, IT-30 (1984), 520. doi: 10.1109/TIT.1984.1056913. Google Scholar
[16]	M. G. Parker, C. Tellambura and K. G. Paterson, Golay complementary sequences,, in, (2003). doi: 10.1002/0471219282.eot367. Google Scholar
[17]	R. Sivaswamy, Multiphase complementary codes,, IEEE Trans. Inform. Theory, IT-24 (1978), 545. Google Scholar
[18]	N. Suehiro and M. Hatori, N-shift cross-orthogonal sequences,, IEEE Trans. Inform. Theory, 34 (1988), 143. doi: 10.1109/18.2615. Google Scholar
[19]	S. M. Tseng and M. R. Bell, Asynchronous multicarrier DS-CDMA using mutually orthogonal complementary sets of sequences,, IEEE Trans. Commun., 48 (2000), 53. doi: 10.1109/26.818873. Google Scholar
[20]	C. C. Tseng and C. L. Liu, Complementary sets of sequences,, IEEE Trans. Inform. Theory, IT-18 (1972), 644. doi: 10.1109/TIT.1972.1054860. Google Scholar
[21]	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 Proc. Letters, 17 (2010), 891. doi: 10.1109/LSP.2010.2068288. Google Scholar
[22]	Z. Y. Zhang, F. X. Zeng and G. X. Xuan, A class of complementary sequences with multi-width zero cross-correlation zone,, IEICE Trans. Fundam., E93-A (2010), 1508. Google Scholar

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References:

[1]	R. Appuswamy and A. K. Chaturvedi, A new framework for constructing mutually orthogonal complementary sets and ZCZ sequences,, IEEE Trans. Inform. Theory, 52 (2006), 3817. doi: 10.1109/TIT.2006.878171. Google Scholar
[2]	L. Bömer and M. Antweiler, Periodic complementary binary sequences,, IEEE Trans. Inform. Theory, 36 (1990), 1487. doi: 10.1109/18.59954. Google Scholar
[3]	H. H. Chen, D. Hank and M. E. Magañz, Design of next-generation CDMA using orthogonal complementary codes and offset stacked spreading,, IEEE Wireless Commun., 2007 (2007), 61. doi: 10.1109/MWC.2007.386614. Google Scholar
[4]	J. H. Chung and K. Yang, New design of quaternary low-correlation zone sequences sets and quaternary Hadamard matrices,, IEEE Trans. Inform. Theory, 54 (2008), 3733. doi: 10.1109/TIT.2008.926406. Google Scholar
[5]	J. A. Davis and J. Jedwab, Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes,, IEEE Trans. Inform. Theory, 45 (1999), 2397. doi: 10.1109/18.796380. Google Scholar
[6]	D. Ž. Đoković, Note on periodic complementary sets of binary sequences,, Des. Codes Cryptogr., 13 (1998), 251. doi: 10.1023/A:1008245823233. Google Scholar
[7]	D. Ž. Đoković, Periodic complementary sets of binary sequences,, Int. Math. Forum, 4 (2009), 717. Google Scholar
[8]	P. Z. Fan and M. Darnell, "Sequence Design for Communications Applictions,'', John Wiley & Sons Inc., (1996). Google Scholar
[9]	P. Z. Fan, W. N. Yuan and Y. F. Tu, Z-complementary binary sequences,, IEEE Signal Proc. Letters, 14 (2007), 509. doi: 10.1109/LSP.2007.891834. Google Scholar
[10]	K. Feng, P. J. S. Shyue and Q. Xiang, On the aperiodic and periodic complementary binary sequences,, IEEE Trans. Inform. Theory, 45 (1999), 296. doi: 10.1109/18.746823. Google Scholar
[11]	R. L. Frank, Polyphase complementary codes,, IEEE Trans. Inform. Theory, IT-26 (1980), 641. doi: 10.1109/TIT.1980.1056272. Google Scholar
[12]	M. J. E. Golay, Complementary series,, IEEE Trans. Inform. Theory, IT-7 (1960), 82. Google Scholar
[13]	S. W. Golomb and G. Gong, "Signal Design for Good Correlation: for Wireless Communications, Cryptography and Radar Applications,'', Cambridge University Press, (2005). doi: 10.1017/CBO9780511546907. Google Scholar
[14]	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
[15]	S. M. Krone and D. V. Sarwate, Quadriphase sequences for spread spectrum multiple-access communication,, IEEE Trans. Inform. Theory, IT-30 (1984), 520. doi: 10.1109/TIT.1984.1056913. Google Scholar
[16]	M. G. Parker, C. Tellambura and K. G. Paterson, Golay complementary sequences,, in, (2003). doi: 10.1002/0471219282.eot367. Google Scholar
[17]	R. Sivaswamy, Multiphase complementary codes,, IEEE Trans. Inform. Theory, IT-24 (1978), 545. Google Scholar
[18]	N. Suehiro and M. Hatori, N-shift cross-orthogonal sequences,, IEEE Trans. Inform. Theory, 34 (1988), 143. doi: 10.1109/18.2615. Google Scholar
[19]	S. M. Tseng and M. R. Bell, Asynchronous multicarrier DS-CDMA using mutually orthogonal complementary sets of sequences,, IEEE Trans. Commun., 48 (2000), 53. doi: 10.1109/26.818873. Google Scholar
[20]	C. C. Tseng and C. L. Liu, Complementary sets of sequences,, IEEE Trans. Inform. Theory, IT-18 (1972), 644. doi: 10.1109/TIT.1972.1054860. Google Scholar
[21]	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 Proc. Letters, 17 (2010), 891. doi: 10.1109/LSP.2010.2068288. Google Scholar
[22]	Z. Y. Zhang, F. X. Zeng and G. X. Xuan, A class of complementary sequences with multi-width zero cross-correlation zone,, IEICE Trans. Fundam., E93-A (2010), 1508. Google Scholar

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