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Metric Mean Dimension and Analog Compression | IEEE Journals & Magazine | IEEE Xplore

Metric Mean Dimension and Analog Compression


Abstract:

Wu and Verdú developed a theory of almost lossless analog compression, where one imposes various regularity conditions on the compressor and the decompressor with the inp...Show More

Abstract:

Wu and Verdú 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.
Published in: IEEE Transactions on Information Theory ( Volume: 66, Issue: 11, November 2020)
Page(s): 6977 - 6998
Date of Publication: 04 May 2020

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