  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.
