| Abstract: |
| Wu and Verd\`{u} 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 \textit{metric
mean dimension}, \textit{mean box dimension} and \textit{mean R\`{e}nyi
information dimension}. An essential tool is the recent Lindenstrauss-Tsukamoto
variational principal expressing metric mean dimension in terms of
certain rate-distortion functions. |
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