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 $|x - y|$.
Publié le : 1975-04-14
Classification:
$\bar d$ and $\bar rho$ distance,
stationary time series,
source coding with a fidelity criterion,
Gaussian time series,
60G35,
94A15,
94A05
@article{1176996402,
author = {Gray, Robert M. and Neuhoff, David L. and Shields, Paul C.},
title = {A Generalization of Ornstein's $\bar d$ Distance with Applications to Information Theory},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 315-328},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996402}
}
Gray, Robert M.; Neuhoff, David L.; Shields, Paul C. A Generalization of Ornstein's $\bar d$ Distance with Applications to Information Theory. Ann. Probab., Tome 3 (1975) no. 6, pp. 315-328. http://gdmltest.u-ga.fr/item/1176996402/