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Rényi’s Information Dimension Beyond I.I.D.

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Co-author: Bernhard C. Geiger (Graz University of Technology)

In 1959, Rényi proposed the information dimension and the d-dimensional entropy to measure the information content of general random variables. Since then, it was shown that the information dimension is of relevance in various areas of information theory, including rate-distortion theory, almost lossless analog compression, or the analysis of interference channels. In this talk, I will propose a generalization of information dimension to stochastic processes, termed information dimension rate. I will then discuss some of its properties and compare it with other generalizations of information dimension available in the literature. I will further show that for Gaussian processes the information dimension rate permits a simple and intuitive characterization in terms of its spectral distribution function.Joint work with Bernhard Geiger (Graz University of Technology).

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