New Uniform Bounds for Almost Lossless Analog Compression
arXiv:1906.07620 · doi:10.1109/ISIT.2019.8849340
Abstract
Wu and Verdú 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 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.
This paper is going to be presented at 2019 IEEE International Symposium on Information Theory. It is a short version of arXiv:1812.00458