Hostname: page-component-84b7d79bbc-c654p Total loading time: 0 Render date: 2024-07-31T14:42:14.221Z Has data issue: false hasContentIssue false
  • English
  • Français

The asymptotics of string matching probabilities for Gaussian random sequences

Published online by Cambridge University Press:  22 January 2016

Shunsuke Ihara  and
Masashi Kubo
Shunsuke Ihara
Affiliation:
School of Informatics and Sciences, Nagoya University, Nagoya 464-8601, Japan, ihara@math.nagoya-u.ac.jp
Masashi Kubo
Affiliation:
Faculty of Education, Tokoha Gakuen University, Shizuoka 420-0911, Japan, kubo@tokoha-u.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Wyner and Ziv (1989) studied the asymptotic properties of recurrence times of stationary ergodic processes, and applied the results to obtain optimal data compression schemes in information transmission. Since then many data compression algorithms based upon string matching of a sequence from an information source with a database have been proposed and studied. In this paper we consider Gaussian stationary processes representing an information source and a database, and study problems of string matching with distortion. We prove theorems concerning the asymptotic behavior of the probability of string matching with distortion and the waiting time for the string matching.

Keywords

60F1060G1594A1594A34
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 166 , June 2002 , pp. 39 - 54
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

References

[BD] Bryc, W. and Dembo, A., Large deviations for quadratic functionals of Gaussian processes, J. Theoretical Prob., 10 (1997), 307–332.CrossRefGoogle Scholar
[BGR] Bercu, B., Gamboa, F. and Rouault, A., Large deviations for quadratic forms of Gaussian stationary processes, Stochastic Process Appl., 71 (1997), 75–90.CrossRefGoogle Scholar
[DZ] Dembo, A. and Zeitouni, O., Large Deviations Techniques and Applications, Jones and Bartlett Pub., Boston, MA, 1992.Google Scholar
[Gr] Gray, R. M., Toeplitz and circulant matrices, Stanford Univ., Tech. Report, 6504-1 (1977).Google Scholar
[GS] Grenander, V. and Szegö, G., Toeplitz Forms and Their Applications, Univ. of California Press, Berkeley, 1958.Google Scholar
[HH] Hida, T. and Hitsuda, M., Gaussian Processes, Amer. Math. Soc., Providence, Rhode Island, 1993.Google Scholar
[I] Ihara, S., Information Theory for Continuous Systems, World Scientific, Singapore, 1993.Google Scholar
[KA] Koga, H. and Arimoto, S., Asymptotic properties of a lossy data compression algorithm with common database, Technical Report of IEICE, IT-118 (1993).Google Scholar
[OW] Ornstein, D. S. and Weiss, B., Entropy and data compression schemes, IEEE Trans. Inform. Theory, IT-39 (1993), 78–83.Google Scholar
[P1] Pinsker, M. S., Amount of information about a Gaussian stationary random process contained in a second process which is stationarily correlated with it, Dokl. Akad. Nauk SSSR, 99 (1954), 213–216.Google Scholar
[P2] Pinsker, M. S., Information and Information Stability of Random Variables and Processes., Holden-Day, San Francisco, 1964.Google Scholar
[S] Shields, P. C., The Ergodic Theory of Discrete Sample Paths, Amer. Math. Soc., Providence, Rhode Island, 1996.Google Scholar
[WZ] Wyner, A. D. and Ziv, J., Some asymptotic properties of the entropy of a stationary ergodic data source with applications to data compression, IEEE Trans. Inform. Theory, IT-35 (1989), 1250–1258.CrossRefGoogle Scholar
[YK] Yang, E.-H. and Kieffer, J. C., On the performance of data compression algorithms based upon string matching, IEEE Trans. Inform. Theory, 44 (1998), 47–65.CrossRefGoogle Scholar