Rate-Distortion Dimension of Stochastic Processes
Abstract
The rate-distortion dimension (RDD) of an analog stationary process is studied as a measure of complexity that captures the amount of information contained in the process. It is shown that the RDD of a process, defined as two times the asymptotic ratio of its rate-distortion function to as the distortion approaches zero, is equal to its information dimension (ID). This generalizes an earlier result by Kawabata and Dembo and provides an operational approach to evaluate the ID of a process, which previously was shown to be closely related to the effective dimension of the underlying process and also to the fundamental limits of compressed sensing. The relation between RDD and ID is illustrated for a piecewise constant process.
Cite
@article{arxiv.1607.06792,
title = {Rate-Distortion Dimension of Stochastic Processes},
author = {Farideh Ebrahim Rezagah and Shirin Jalali and Elza Erkip and H. Vincent Poor},
journal= {arXiv preprint arXiv:1607.06792},
year = {2016}
}
Comments
Presented at 2016 IEEE International Symposium on Information Theory