Joint work with Adam Śpiewak
Wu and Verdú developed a theory for almost lossless analog
compression
where one imposes various regularity conditions on the compressor
and the decompressor and the input signal is modeled by a (typically
infinite-entropy) Bernoulli process. In this work we consider the
broader class of signals modeled by time-invariant probability measures
and find uniform lower and upper bounds in terms of metric
mean dimension, mean box dimension and mean Rényi
information dimension. An essential tool is the recent
Lindenstrauss-Tsukamoto
variational principal expressing metric mean dimension in terms of
certain rate-distortion functions.