Advertisement

Error Probabilities for Identification Coding and Least Length Single Sequence Hopping

  • Edward C. van der Meulen
  • Sándor Csibi
Chapter

Abstract

Upper and lower bounds on the probabilities of the missed and the false identification are proved for Poisson population, for multiple access with least length single sequence hopping, and identification plus transmission coding at each potential source. False identification due to possible worst pairs of identifiers is considered. It is shown, how can one drastically suppress the probability of this event provided not just a single code word but at least a couple of code words might be sent from each source, following each demand, consecutively. An approriate kind of randomization is assumed for this purpose, frequently needed anyhow. The combination of identification plus transmission coding and single sequence hopping might be appealing for certain tasks of identification through a multiple access channel. This might be the case, e.g., for certain public emergency services, meant to convey within some area many kinds of occasional demands from a vast population of potential sources, each sending a very short message following a demand, very infrequently.

Keywords

Single Sequence Code Word False Identification Multiple Access Channel Message Block 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. Ahlswede and G. Dueck, “Identification via channels,” IEEE Trans. on Inform Theory, IT-35, no. 1, 1989, pp. 15–29.MathSciNetCrossRefGoogle Scholar
  2. [2]
    T.S. Han and S. Verdii, “New results in the theory of identification via channels,” IEEE Trans. Inform. Theory, IT-38, no. 1, 1992, pp. 14–25.CrossRefGoogle Scholar
  3. [3]
    S. Verdú and V.K. Wei, “Explicit constructions of constant-weight codes for identification via channels,” IEEE Trans. on Inform. Theory, IT-39, no. 1, 1993, pp. 30–36, 1993.CrossRefGoogle Scholar
  4. [4]
    R. Ahlswede, “General Theory of Information Transfer,” Preprint 97–118, Sonderforschungsbereich 343, Diskrete Strukturen in der Mathematik Universität Bielefeld, D, 1997.Google Scholar
  5. [5]
    R.E. Blahut, Theory and Practice of Error Control Codes. Reading, MA: Addison-Wesley Publ. Co., 1983.MATHGoogle Scholar
  6. [6]
    N. Abramson “Development of ALOHANET,” IEEE Trans. on Inform. Theory, vol. 31, 1985, pp. 119–123.MATHCrossRefGoogle Scholar
  7. [7]
    N. Abramson “Multiple access in wireless digital networks,” Proc. IEEE, vol. 82, 1994, pp. 1360–1370.CrossRefGoogle Scholar
  8. [8]
    L. Pap, “Performance analysis of DS unslotted packet radio networks with given auto- and crosscorrelation sidelobes,” Proc. IEEE Third Internat. Symp. Spread Spectrum Techniques and Applications, Oulu, Finland, 1994, pp. 343–345.Google Scholar
  9. [9]
    S. Csibi, “Two-sided bounds on the decoding error probability for structured hopping, single common sequence and Poisson population,” Proc. 1994 IEEE Internat. Symp. on Inform. Theory, Trondheim, 1994, p. 290.Google Scholar
  10. [10]
    S. Csibi, “On the least decoding error probability for truly asynchronous single sequence hopping,” Proc. 1995 IEEE Internat. Symp. on Inform. Theory, Whistler, 1995, p. 385.CrossRefGoogle Scholar
  11. [11]
    E. C. van der Meulen and S. Csibi, “Identification coding for least length single sequence hopping,” Abstracts, 1996 IEEE Information Theory Workshop, Dan-Carmel, Haifa, 1996, p. 67.Google Scholar
  12. [12]
    L.A. Bassalygo and M.S. Pinsker, “Limited multiple-access to an asynchronous channel,” Problems of Information Transmission, (in Russian) Vol. 19, 1983, pp. 92–96.MATHGoogle Scholar
  13. [13]
    Q.A. Nguyen, L. Györfi, and J.L.Massey. “Constructions of binary constant weight cyclic codes and cyclically permutable codes,” IEEE Trans. on Inform Theory, IT-38, 1992, pp. 940–949.Google Scholar
  14. [14]
    S. Csibi, “On the decoding error probability of slotted asynchronous access and least length single sequence hopping,” Preprint, 1997.Google Scholar
  15. [15]
    S. Csibi, “On the decoding error probability of truly asynchronous least length single sequence hopping,” Preprint, 1997.Google Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Edward C. van der Meulen
    • 1
  • Sándor Csibi
    • 2
  1. 1.Dept. of Math.Catholic University of LeuvenHeverleeBelgium
  2. 2.Dept. of Telecom.Techn. Univ. of BudapestBudapestHungary

Personalised recommendations