A Generalization of Ornstein's $\bar d$ Distance with Applications to Information Theory

Robert M. Gray, David L. Neuhoff, and Paul C. Shields
Source: Ann. Probab. Volume 3, Number 2 (1975), 315-328.

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 $|x - y|$.

First Page:
Primary Subjects: 60G35
Secondary Subjects: 94A15, 94A05
Full-text: Open access