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
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
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