Abstract
This paper presents three new sets of frequency hopping sequences, which are converted into sequences for CDMA. One of the CDMA sequence families is optimal with respect to the Welch bound, and two are nearly optimal. Our sequences are available for more lengths, and have much higher linear complexity than other CDMA sequences. They have a similar structure to the small Kasami set, but are balanced. The CDMA sequences are constructed using a composition method, which combines new shift sequences with pseudonoise columns to form an array. The array dimensions are relatively prime, so it is unfolded using the Chinese Remainder Theorem.
Each of our constructions gives rise to two additional families with larger family sizes but worse correlation as explained in Section 4.2.
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References
Games, R.A.: Crosscorrelation of M-sequences and GMW-sequences with the same primitive polynomial. Discrete Applied Mathematics 12(2), 139–146 (1985)
Baumert, L.D.: Cyclic difference sets. Springer (1971)
Weng, L.J.: Decomposition of M-sequences and its applications. IEEE Trans. Inform. Theory 17, 457–463 (1971)
MacWilliams, F.J., Sloane, N.J.A.: Pseudo-Random Sequences and Arrays. Proc. IEEE 64(12), 1715–1729 (1976)
Tirkel, A.Z., Osborne, C.F., Hall, T.E.: Steganography-Applications of coding theory. In: IEEE Information Theory Workshop, Svalbard, Norway, pp. 57–59 (1997)
Tirkel, A.Z., Hall, T.E.: New Matrices with good Auto and Cross-Correlation. In: IWSDA 2005, Japan, pp. 51–55 (2005)
Moreno, O., Tirkel, A.Z.: Multi-Dimensional Arrays for Watermarking. In: ISIT 2011, St Petersburg, Russia, pp. 2667–2671 (2011)
Moreno, O., Tirkel, A.Z.: Digital Watermarking WO2011/050390 (2010)
Golomb, S.W., Taylor, H.: Construction and properties of Costas arrays. Proc. IEEE 72(9), 1143–1163 (1984)
Moreno, O., Omrani, R., Maric, S.V.: A New Construction of Multiple Target Sonar and Extended Costas Arrays with Perfect Correlation. In: 40th Annual Conference on Information Sciences and Systems, March 22-24, pp. 512–517 (2006)
Kumar, P.V.: On the Existence of Square Dot-Matrix Patterns Having a Special Three-Valued Periodic Correlation Function. IEEE Trans. Inform. Theory 34, 271–277 (1988)
Moreno, O.: Survey of Results on Signal Patterns for Locating One or Multiple Targets. In: Difference Sets, Sequences and Their Correlation Properties. NATO Science Series, vol. 542, pp. 353–368 (1999)
Mac Williams, F.J., Sloane, N.J.A.: The Theory of Error Correcting Codes. North-Holland, Amsterdam (1977)
Sarwate, D.V., Pursley, M.B.: Crosscorrelation Properties of Pseudorandom and Related Sequences. Proc. IEEE 68(5), 593–619 (1980)
Zeng, X., Liu, J.Q., Hu, L.: Generalized Kasami Sequences: The Large Set. Proc. IEEE-IT 53(7), 2587–2598 (2007)
Tirkel, A., Hall, T., Osborne, C., Meinhold, N., Moreno, O.: Collusion Resistant Fingerprinting of Digital Audio. In: SIN 2011, Sydney, November 14-16, pp. 5–12 (2011)
Boztas, S.: Lower bounds on the maximum periodic and aperiodic correlation of signal sets with arbitrary energy distribution. In: Proc. of the International Symposium on Information Theory and Its Applications, Sydney, Australia, November 20-25, pp. 1007–1012 (1994)
Stular, M., Tomazic, S.: Maximum periodic correlation of pseudo-random sequences in CDMA. In: MEleCon 2000, vol. I, pp. 420–423 (2000)
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Moreno, O., Tirkel, A. (2012). New Optimal Low Correlation Sequences for Wireless Communications. In: Helleseth, T., Jedwab, J. (eds) Sequences and Their Applications – SETA 2012. SETA 2012. Lecture Notes in Computer Science, vol 7280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30615-0_20
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DOI: https://doi.org/10.1007/978-3-642-30615-0_20
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