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Rate-distortion dimension of stochastic processes

Author(s): Rezagah, Farideh Ebrahim; Jalali, Shirin; Erkip, Elza; Poor, H Vincent

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 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 R(D) to log 1/D as the distortion D 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. Publication Date: 2016 Citation: Rezagah, Farideh Ebrahim, Shirin Jalali, Elza Erkip, and H. Vincent Poor. "Rate-distortion dimension of stochastic processes." In 2016 IEEE International Symposium on Information Theory (ISIT), pp. 2079-2083. IEEE, 2016. doi:10.1109/ISIT.2016.7541665 DOI: 10.1109/ISIT.2016.7541665 EISSN: 2157-8117 Pages: 2079 - 2083 Type of Material: Conference Article Journal/Proceeding Title: 2016 IEEE International Symposium on Information Theory (ISIT) Version: Author's manuscript

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