Metric mean dimension and analog compression
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.
Cite
@article{arxiv.1812.00458,
title = {Metric mean dimension and analog compression},
author = {Yonatan Gutman and Adam Śpiewak},
journal= {arXiv preprint arXiv:1812.00458},
year = {2022}
}
Comments
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