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.
Presented in part at IEEE Intern. Workshop on Inform. Theory, Haifa, Israel, June 9–14, 1996. Research of both authors was partially supported by 1995–98, Project Math. Inform. Theory of the Royal Belgian Ac. Sc., Letts. and Fine Arts, and the Hung. Ac. of Sc.
Research was partially supported also by the Hung. Nat. Sc. Res. Found. Grant No. OTKA 11601–206.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. Ahlswede and G. Dueck, “Identification via channels,” IEEE Trans. on Inform Theory, IT-35, no. 1, 1989, pp. 15–29.
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.
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.
R. Ahlswede, “General Theory of Information Transfer,” Preprint 97–118, Sonderforschungsbereich 343, Diskrete Strukturen in der Mathematik Universität Bielefeld, D, 1997.
R.E. Blahut, Theory and Practice of Error Control Codes. Reading, MA: Addison-Wesley Publ. Co., 1983.
N. Abramson “Development of ALOHANET,” IEEE Trans. on Inform. Theory, vol. 31, 1985, pp. 119–123.
N. Abramson “Multiple access in wireless digital networks,” Proc. IEEE, vol. 82, 1994, pp. 1360–1370.
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.
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.
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.
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.
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.
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.
S. Csibi, “On the decoding error probability of slotted asynchronous access and least length single sequence hopping,” Preprint, 1997.
S. Csibi, “On the decoding error probability of truly asynchronous least length single sequence hopping,” Preprint, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
van der Meulen, E.C., Csibi, S. (2000). Error Probabilities for Identification Coding and Least Length Single Sequence Hopping. In: Althöfer, I., et al. Numbers, Information and Complexity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6048-4_19
Download citation
DOI: https://doi.org/10.1007/978-1-4757-6048-4_19
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4967-7
Online ISBN: 978-1-4757-6048-4
eBook Packages: Springer Book Archive