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.