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arXiv · 1812.00458

Metric mean dimension and analog compression

Yonatan Gutman·Adam Śpiewak
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Abstract

Wu and Verd\'u developed a theory of almost lossless analog compression, where one imposes various regularity conditions on the compressor and the decompressor with the input signal being modelled by a (typically infinite-entropy) stationary stochastic process. In this work we consider all stationary stochastic processes with trajectories in a prescribed set of (bi-)infinite sequences and find uniform lower and upper bounds for certain compression rates in terms of metric mean dimension and mean box dimension. An essential tool is the recent Lindenstrauss-Tsukamoto variational principle expressing metric mean dimension in terms of rate-distortion functions. We obtain also lower bounds on compression rates for a fixed stationary process in terms of the rate-distortion dimension rates and study several examples.

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Yonatan Gutman, Adam Śpiewak. 2018-12-02. Metric mean dimension and analog compression. https://doi.org/10.1109/tit.2020.2992388

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