分碼多工存取(Code-division multiple-access)的技術已經被廣泛的使用在手機的通訊系統上。在傳統的CDMA系統上，每位使用者都會有一組正交的展頻碼來避免多使用者之間的互相干擾。一旦使用者之間的同步有誤差或是有多路徑效應的時候，多使用者之間傳的訊號就不再是正交，而會有互相干擾的情況發生。為了避免這個問題，零相關區間序列(Zero Correlation Zone Sequences)被提了出來。零相關區間序列被用來當作CDMA系統的展頻碼的時候，只要同步的誤差和多路徑的效應在一定的範圍之內，多使用者干擾和多路徑干擾都可以被消除掉。
在這篇論文裡，我們提出了一個直接由布林函數造出零相關區間序列的方法。像是之前所提出來的方法，大部分都需要特殊的序列來組合出零相關區間序列。我們的造法只需要做一些排列組合和分區的運算就可以得到想要的序列，不需要先有特殊的序列才能造出零相關區間序列。在我們的方法裡面，序列的長度和數量、信號分佈和零相關區間的長度都可以很自由的調整。而且我們所造出來的序列的零相關區間的長度也可以達到或是接近理論值的上限。藉由布林函數的結構，我們所造出來的序列可以有低複雜度的編碼器。我們的方法也可以造出完美序列。另外，在特殊的參數的情況下，我們還可以產生一組零相關區間序列，而且每一個序列都是完美序列。所以我們所提出來的方法，很適合用在新一代的CDMA系統上。

In this thesis, new direct constructions of zero correlation zone (ZCZ) sequence sets from the generalized Boolean functions are proposed. Di®erent from previous results in the literature, our methods do not require other special sequences for the constructions. The sequence length, the length of the ZCZ, the set size, and the constellation size are all very flexible. Optimal and almost optimal ZCZ sequences can be obtained from the proposed constructions. In addition, a construction of perfect sequences is also provided in the thesis.

[1] R. L. Frank and S. A. Zadoff, "Phase shift pulse codes with good periodic correlation properties," IEEE Trans. Inf. Theory, vol. IT-8, pp. 381-382, Oct. 1962.
[2] C. Chu, "Polyphase codes with good periodic correlation properties," IEEE Trans. Inf. Theory, vol. IT-18, pp. 531{532, July 1972.
[3] N. Suehiro and M. Hatori, "Modulatable orthogonal sequences and their application to SSMA systems," IEEE Trans. Inf. Theory, vol. 34, pp. 93-100, Jan. 1988.
[4] B. M. Papovic, "Generalized chirp-like polyphase sequences with optimum correlation properties," IEEE Trans. Inf. Theory, vol. 38, pp. 1406-1409, July 1992.
[5] L. R. Welch, "Lower bounds on the maximum cross correlation of signals," IEEE Trans. Inf. Theory, vol. IT-20, pp. 397-399, May 1974.
[6] P. Z. Fan, N. Suehiro, N. Kuroyanagi, and X. M. Deng, "Class of binary sequences with zero correlation zone," Electron. Lett., vol. 35, no. 10, pp. 777-779, May 1999.
[7] X. M. Deng and P. Z. Fan, "Spreading sequence sets with zero correlation zone," Electron. Lett., vol. 36, no. 11, pp. 993-994, May 2000.
[8] X. H. Tang, P. Z. Fan, D. B. Li, and N. Suehiro, "Binary array set with zero correlation zone," Electron. Lett., vol. 37, no. 13, pp. 841-842, June 2001.
[9] K. Takatsukasa, S. Matsufuji, and N. Kuroyanagi, "Ternary ZCZ sequence sets for cellular CDMA systems," IEICE Trans. Fund., vol. E85-A, pp. 2135-2140, Sept. 2002.
[10] S. Matsufuji, N. Kuroyanagi, N. Suehiro, and P. Z. Fan, "Two types of polyphase sequence sets for approximately synchronized CDMA systems," IEICE Trans. Fund., vol. E86-A, pp. 229-234, Jan. 2003.
[11] H. Torii, M. Nakamura, and N. Suehiro, "A new class of zero-correlation zone sequences," IEEE Trans. Inf. Theory, vol. 50, pp. 559-565, Mar. 2004.
[12] A. Rathinakumar and A. K. Chaturvedi, "Mutually orthogonal sets of ZCZ sequences," Electron. Lett., vol. 40, no. 18, pp. 1133-1134, Sept. 2004.
[13] T. Hayashi and S. Matsufuji, "Sets of zero-correlation zone sequence pairs," in Proc. Int. Workshop Signal Design and its Applicat. in Commun., Shimonoseki, Japan, Oct. 2005, pp. 78-81.
[14] X. H. Tang, "ZCZ sequences construction from perfect sequences based on interleave technique," in Proc. Int. Workshop Signal Design and its Applicat. in Commun., Shimonoseki, Japan, Oct. 2005, pp. 82-85.
[15] X. H. Tang and W. H. Mow, "Design of spreading codes for quasisynchronous CDMA with intercell interference," IEEE J. Sel. Areas Commun., vol. 24, pp. 84-93, Jan. 2006.
[16] R. Appuswamy and A. K. Chaturvedi, "A new framework for constructing mutually orthogonal complementary sets and ZCZ sequences," IEEE Trans. Inf. Theory, vol. 52, pp. 3817-3826, Aug. 2006.
[17] H. Torii and M. Nakamura, "Enhancement of ZCZ sequence set construction procedure," IEICE Trans. Fund., vol. E90-A, pp. 535-538, Feb. 2007.
[18] C. Han, T. Hashimoto, and N. Suehiro, "Poly phase zero-correlation zone sequences based on complete complementary codes and DFT matrix," in Proc. Int. Workshop Signal Design and its Applicat. in Commun., Chengdu, China, Sept. 2007, pp. 172-175.
[19] C. Han, T. Hashimoto, and N. Suehiro, "A novel construction method of zero-correlation zone sequences based on complete complementary codes," in Proc. IEEE Int. Symp. Inform. Theory, Toronto, Canada, July 2008, pp. 1931-1934.
[20] Z. Zhou, X. Tang, and G. Gong, "A new class of sequences with zero or low correlation zone based on interleaving technique," IEEE Trans. Inf. Theory, vol. 54, pp. 4267-4273, Sept. 2008.
[21] C.-W. Chen, Y.-C. Liu, and Y. T. Su, "Systematic constructions of zero-correlation zone sequences," in Proc. IEEE Int. Symp. Inform. Theory, Seoul, Korea, June 2009, pp. 119-123.
[22] R. De Gaudenzi, C. Elia, and R. Viola, "Bandlimited quasi-synchronous CDMA: A novel satellite access technique for mobile and personal communication systems," IEEE J. Sel. Areas Commun., vol. 10, pp. 328-343, Feb. 1992.
[23] B. Long, P. Zhang, and J. Hu, "A generalized QS-CDMA system and the design of new spreading codes," IEEE Trans. Veh. Technol., vol. 47, pp. 1268-1275, Nov. 1998.
[24] P. Z. Fan, "Spreading sequence design and theoretical limits for quasisynchronous CDMA systems," EURASIP J. Wireless Commun. and Networking, no. 1, pp. 19-31, 2004.
[25] N. Suehiro, "A signal design without co-channel interference for approximately synchronized CDMA systems," IEEE J. Sel. Areas Commun., vol. 12, pp. 837-841, June 1994.
[26] P. Z. Fan and L. Hao, "Generalized orthogonal sequences and their applications insynchronous CDMA systems," IEICE Trans. Fund., vol. E89-A, pp. 2054-2066, Nov. 2000.
[27] E. I. Krengel, "New binary ZCZ sequence sets with mismatched fltering," in Proc. Int. Workshop Signal Design and its Applicat. in Commun., Chengdu, China, Sept. 2005, pp. 26-29.
[28] A. Z. Tirkel, E. I. Krengel, and T. E. Hall, "Sequences with large zcz," in Proc. Int. Symp. on Spread Spectrum Tech. and Applications., Sydney, Australia, Aug. 2004, pp. 270-274.
[29] K. Ohue and T. Uto, "A generation method of orthogonal periodic complex number sequence sets with periodic zero cross-correlation zones for any period," IEICE Trans. Fund., vol. J39-A, pp. 1185-1197, June 2006.
[30] X. H. Tang, P. Z. Fan, and S. Matsufuji, "Lower bounds on correlation of spreading sequence set with low or zero correlation zone," Electron. Lett., vol. 36, no. 13, pp. 551-552, Mar. 2000.
[31] S. Matsufuji, N. Suehiro, N. Kuroyanagi, and P. Z. Fan, "Spreading sequence sets for approximately synchronized cdma system with no co-channel interference and high data capacity," in Proc. 2nd Int. Symp. Wireless Personal Multimedia Commun., Amsterdam, Netherlands, Sept. 1999, pp. 333-339.
[32] C.-C. Tseng and C. L. Liu, "Complementary sets of sequences," IEEE Trans. Inf. Theory, vol. IT-18, pp. 644-652, Sept. 1972.
[33] N. Suehiro and M. Hatori, "N-shift cross-orthogonal sequences," IEEE Trans. Inf. Theory, vol. 34, pp. 143-146, Jan. 1988.
[34] F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1977.
[35] K. G. Paterson, "Generalized Reed-Muller codes and power control in OFDM modulation," IEEE Trans. Inf. Theory, vol. 46, pp. 104-120, Jan. 2000.
[36] C.-Y. Chen, C.-H. Wang, and C.-C. Chao, "Complete complementary codes and generalized Reed-Muller codes," IEEE Commun. Lett., vol. 12, pp. 849-851, Nov. 2008.
[37] C.-Y. Chen, "Complementary sets, complete complementary codes, and their applications," Ph.D. dissertation, Inst. Commun. Eng., National Tsing Hua Univ., Hsinchu, Taiwan, 2009.