# New Uniform Bounds for Almost Lossless Analog Compression

## TL;DR

This paper establishes uniform bounds on almost lossless analog compression rates for stationary processes within a set, linking these bounds to metric mean dimension and mean box dimension, and utilizing a variational principle for rate-distortion functions.

## Contribution

It introduces uniform bounds for compression rates of stationary processes based on metric mean dimension and mean box dimension, extending prior theories.

## Key findings

- Derived lower and upper bounds for compression rates
- Connected metric mean dimension with rate-distortion functions
- Applied variational principle to analyze compression limits

## 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 $\mathcal{S} \subset [0,1]^\mathbb{Z}$ 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.