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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
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Abstract

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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

Information

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

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