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Paper Detail

Paper Title New Uniform Bounds for Almost Lossless Analog Compression
Paper IdentifierWE2.R7.5
Authors Yonatan Gutman, Polish Academy of Sciences, Poland; Adam Śpiewak, University of Warsaw, Poland
Session Lossless Compression II
Location Bièvre, Level 5
Session Time Wednesday, 10 July, 11:40 - 13:20
Presentation Time Wednesday, 10 July, 13:00 - 13:20
Manuscript  Click here to download the manuscript
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 $\mS \subset [0,1]^\Z$ of (bi)infinite sequences and find uniform lower and upper bounds for certain compression rates in terms of \textit{metric mean dimension} and \textit{mean box dimension}. An essential tool is the recent Lindenstrauss-Tsukamoto variational principle expressing metric mean dimension in terms of rate-distortion functions.