Open Access
Translator Disclaimer
April, 1975 A Generalization of Ornstein's $\bar d$ Distance with Applications to Information Theory
Robert M. Gray, David L. Neuhoff, Paul C. Shields
Ann. Probab. 3(2): 315-328 (April, 1975). DOI: 10.1214/aop/1176996402

Abstract

Ornstein's $\bar{d}$ distance between finite alphabet discrete-time random processes is generalized in a natural way to discrete-time random processes having separable metric spaces for alphabets. As an application, several new results are obtained on the information theoretic problem of source coding with a fidelity criterion (information transmission at rates below capacity) when the source statistics are inaccurately or incompletely known. Two examples of evaluation and bounding of the process distance are presented: (i) the $\bar{d}$ distance between two binary Bernoulli shifts, and (ii) the process distance between two stationary Gaussian time series with an alphabet metric $|x - y|$.

Citation

Download Citation

Robert M. Gray. David L. Neuhoff. Paul C. Shields. "A Generalization of Ornstein's $\bar d$ Distance with Applications to Information Theory." Ann. Probab. 3 (2) 315 - 328, April, 1975. https://doi.org/10.1214/aop/1176996402

Information

Published: April, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0304.94025
MathSciNet: MR368127
Digital Object Identifier: 10.1214/aop/1176996402

Subjects:
Primary: 60G35
Secondary: 94A05 , 94A15

Keywords: $\bar d$ and $\bar rho$ distance , Gaussian time series , source coding with a fidelity criterion , stationary time series

Rights: Copyright © 1975 Institute of Mathematical Statistics

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.3 • No. 2 • April, 1975
Back to Top