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 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.

v3: Accepted for publication in IEEE Transactions on Information Theory. Additional examples were added. Material have been reorganized (with some parts removed). Minor mistakes were corrected

References in corpus (4)

• Rate distortion theory, metric mean dimension and measure theoretic entropy
• New Uniform Bounds for Almost Lossless Analog Compression
• Variational principles for amenable metric mean dimensions
• Application of signal analysis to the embedding problem of ${\mathbb{Z}}^k$-actions

Cited by in corpus (4)

• Around the variational principle for metric mean dimension
• A variational principle for the metric mean dimension of level sets
• On variational principles for metric mean dimension
• Metric mean dimension via subshifts of compact type