Abstract
Cross-bifix-free sets are sets of bifix-free sequences with the property that no prefix of any sequence is a suffix of any other sequence. This paper presents a general construction method for cross-bifix-free sequences based on kernels. The cardinality of cross-bifix-free sets follows the Fibonacci progression. A simplified method, applicable to a limited number of so-called “regular kernel sets”, is proposed as well. Properties of such sequences with an outline for further research are discussed.
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Notes
Here and elsewhere below, we shall say that simulation occurs when a segment of the data - which may be considered to be random—happens to reproduce a suffix or prefix of a synchronization sequence.
References
Choi, D.-W.: Frame Alignment in a Digital Carrier System–A Tutorial. IEEE Comm. Mag. 28, 47–54 (1990)
Eu, J.H., Rollins, W.W.: ‘A Performance Review of Out-of-Frame Detection Schemes for DS1 Signals. IEEE Trans. on Comm. 39, 1004–1009 (1991)
Jones, E.V., Al-Subbahg, M.N.: Algorithms for frame alignment–some comparisons. IEE Proc. part F - Commun., Radar & Signal processing 132(7), 529–536 (1985)
Munhoz, D.T.R., Roberto, J., de Marca, B., Arantes, D.S.: On Frame Synchronization of PCM Systems. IEEE Trans. on Comm. 28, 1213–1218 (1980)
Kang, K., Bailey, M.P., Eu, J.H.: Statistical Properties of Out-of-Frame Detection Schemes for Digital Transmission Systems. IEEE Trans. on Comm. 40, 980–987 (1992)
Massey, J.L.: Optimum Frame Synchronization. IEEE Trans. on Comm. 20, 115–119 (1972)
Lui, G.L., Tan, H.H.: Frame Synchronization for Gaussian Channels. IEEE Trans. on Comm. 35, 818–828 (1987)
De Fina, S.: Simultaneous Frame and Bit Synchronization of HF Receivers by Constatant False Alarm Methods. European Trans. on Telecom 7(1), 83–92 (1996)
Dodds, D.E., Button, L.R., Pan, S.-M.: ‘Robust Frame Synchronization for Noisy PCM Systems. IEEE Trans. on Comm. 33, 465–469 (1985)
Dodds, D.E., Pan, S.-M., Wacker, G.W.: Statistical distribution of PCM Framing Times. IEEE Trans. on Comm. 36, 1236–1241 (1988)
Hershey, J.E., Michaelis, A.D.: Multiplexed Synchronization: An Electronic Warfare Countermeasure. IEEE Trans. on Comm. 39, 1010–1018 (1991)
Lindner, J.: Binary sequences up to length 40 with best possible autocorrelation function. Electron. Lett. 11, 507 (1975)
Al-Subbagh, M.N., Jones, E.V.: Optimum patterns for frame alignment. IEE Proc. part F - Commun. Radar & Signal processing 135(6), 594–603 (December 1988)
Dragana Bajić, Dusan Drajić: On The Optimal Frame Synchronization Markers for Channels with Memory, IEEE Transactions on Communications, 1995, Vol. 43, No. 2/3/4, pp. 1256–1258,
Häberle, H.: Frame synchronizing PCM systems. Electrical Communications 44(4), 280–287 (1969)
CCITT Recommendation, Blue Book III.4, Genève 1988.
ITU-T Recommendations G. 783, Section 2.2.2, Helsinki, 1–12 March 1993.
ITU-T Recommendation G.709 (2003),
D. Bajic, “On Construction of Cross-Bifix-Free Kernel Sets,” 2nd MCM COST 2100, TD(07)237, Lisbon, Portugal, February 2007
Stefano Bilotta, Elisa Pergola, and Renzo PinzaniIEEE A New Approach to Cross-Bifix-Free Sets TRANSACTIONS ON INFORMATION THEORY, VOL. 58, NO. 6, JUNE 2012
Yeow Meng Chee, Han Mao Kiah, Punarbasu Purkayastha, Chengmin Wang, Cross-Bifix-Free Codes within a Constant Factor of Optimality, submitted to IEEE Trans. on IT
Unger, S.H.: A theorem on self-overlapping sequences. The Am. Mathematical monthly 67, 139–143 (1960)
Nielsen, P.T.: On the Expected Duration of a Search for a Fixed Pattern in Random Data. IEEE Trans. on Inf. Theory. 19, 702–704 (1973)
T. McConell: “The Expected Time to Find a String in a Random Binary Sequence” [http://barnyard.syr.edu/cover.pdf], January 2001.
Bajić, D., Drajić, D.: Duration of search for a fixed pattern in random data: Distribution function and variance. Electronics Letters 31(8), 631–632 (1995)
D. Bajić, J. Stojanovic and J. Lindner: “Multiple Window-sliding Search”, Proceedings of 2003 I.E. International Symposium on Information Theory ISIT-2003, Yokohama, Japan, June 2003, pp 249
Dragana Bajić, Jakov Stojanović: “Distributed Sequences and Search Process”. IEEE International Conference on Communications ICC2004, Paris, France, June 2004, pp 514–518, ISBN: 0-7803-8534-9
Stefanovic, C., Bajic, D.: On the Search for a Sequence from a Predefined Set of Sequences in Random and Framed Data Streams. IEEE Transactions on Communications 60(1), 189–197 (January 2012)
A. J. de Lind van Wijngaarden, T. J. Willink: “Frame Synchronization Using Distributed Sequences”, IEEE Transactions on Communications, 2000, Vol. 48, No. 12, pp 2127–2138
Dragana Bajić, V. Senk, M. Despotovic:: Subsets of the STM-1 frame-alignment signal: a monitoring analysis, IEE Proceedings, Communications, 2002, Vol. 149, No. 5, str. 242–248, ISSN 1350–2425.
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The authors wish to thank the unknown Referee for his helpful and inspiring comments.
This paper is funded in part by Grants TR32040, Ministry of Science, Serbia and 114-451-2061/2011-01 of APV; it is an outcome of COST 2100 and IC1004 Actions.
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Bajic, D., Loncar-Turukalo, T. A simple suboptimal construction of cross-bifix-free codes. Cryptogr. Commun. 6, 27–37 (2014). https://doi.org/10.1007/s12095-013-0088-8
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DOI: https://doi.org/10.1007/s12095-013-0088-8