Statistical Analysis of Search for Set of Sequences in Random and Framed Data

  • Dragana Bajić
  • Čedomir Stefanović
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6338)


In this paper we analyze the search for a set of predefined sequences in random and framed data and derive a number of corresponding statistical parameters. Most importantly, we derive probability mass function of the search process from which all moments can obtained. The presented solution is based on sequences’ descriptors called cross-bifices, which express similarities among sequences in the set. The derived results can be used to evaluate the properties of frame-synchronization sequences.


synchronization sequences frame synchronization 


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  1. 1.
    Nielsen, P.T.: On the Expected Duration of a Search for a Fixed Pattern in Random Data. IEEE Trans. Inform. Theory 19, 702–704 (1973)zbMATHCrossRefGoogle Scholar
  2. 2.
    Scholtz, R.: Frame Synchronization Techniques. IEEE Trans. Comm. 28, 1204–1213 (1980)CrossRefGoogle Scholar
  3. 3.
    Georghiades, C.N., Snyder, D.L.: Locating Data Frames in Direct-Detection Optical Communication Systems. IEEE Trans. Comm. 32, 118–123 (1984)CrossRefGoogle Scholar
  4. 4.
    Lui, G.L., Tan, H.H.: Frame Synchronization for Direct-Detection Optical Communications. IEEE Trans. Comm. 34, 227–237 (1986)CrossRefGoogle Scholar
  5. 5.
    Al-Subbagh, M.N., Jones, E.V.: Optimum patterns for frame alignment. IEE Proc. part F - Commun., Radar & Signal Processing 135(6), 594–603 (1988)CrossRefGoogle Scholar
  6. 6.
    Patarasen, S., Gheorghiades, C.N.: Frame Synchronization for Optical Overlapping Pulse-Position Modulation Systems. IEEE Trans. Comm. 40, 783–794 (1992)zbMATHCrossRefGoogle Scholar
  7. 7.
    de Lind van Wijngaarden, A.J., Willink, T.J.: Frame Synchronization Using Distributed Sequences. IEEE Trans. Comm. 48(12), 2127–2138 (2000)CrossRefGoogle Scholar
  8. 8.
    Newton, N.J.: Data Synchronization and Noisy Environments. IEEE Trans. Inform. Theory 48(8), 2253–2262 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Chiani, M., Martini, M.G.: On Sequential Frame Synchronization in AWGN Channels. IEEE Trans. Comm. 54(2), 339–348 (2006)CrossRefGoogle Scholar
  10. 10.
    Villanti, M., Iubatti, M., Corazza, A.V.C.G.E.: Design of Distributed Unique Words for Enhanced Frame Synchronization. IEEE Trans. Comm. 57(8), 2430–2440 (2009)CrossRefGoogle Scholar
  11. 11.
  12. 12.
    Bajic, D., Stefanovic, C., Vukobratovic, D.: Search Process and Probabilistic Bifix Approach. In: Proc. of IEEE ISIT 2005. Adelaide, Australia (September 2005)Google Scholar
  13. 13.
    Stefanovic, C.: Synchronization sequences and bifix analysis (in Serbian). Master’s thesis, Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia (2006)Google Scholar
  14. 14.
    Bajic, D., Drajic, D.: Duration of a search for a fixed pattern in random data: Distribution function and variance. Electron. Lett. 31(8), 631–632 (1995)CrossRefGoogle Scholar
  15. 15.
    Bajic, D., Stojanovic, J.: Distributed Sequences and Search Process. In: Proc. of IEEE ICC 2004, Paris, France (June 2004)Google Scholar
  16. 16.
    CCITT Recommendation, C.: Blue Book III.4. Geneve, Switzerland (1988)Google Scholar
  17. 17.
    Weindl, J., Hagenauer, J.: Applying Techniques from Frame Synchronization for Biological Sequence Analysis. In: Proc. of IEEE ICC 2007, Glasgow, Scotland (June 2007)Google Scholar
  18. 18.
    Weindl, J.: Frame Synchronization Processes in Gene Expression. Ph.D. thesis, Technischen Universität München, Munich, Germany (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Dragana Bajić
    • 1
  • Čedomir Stefanović
    • 1
  1. 1.Department of Power, Electronics and Communication EngineeringUniversity of Novi SadNovi SadSerbia

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