Almost lossless analog signal separation

Authors

David Stotz, Erwin Riegler, and Helmut Bölcskei

Reference

Proc. of IEEE International Symposium on Information Theory (ISIT), Istanbul, Turkey, pp. 106-110, July 2013.

DOI: 10.1109/ISIT.2013.6620197

Abstract

We propose an information-theoretic framework for analog signal separation. Specifically, we consider the problem of recovering two analog signals from a noiseless sum of linear measurements of the signals. Our framework is inspired by the groundbreaking work of Wu and Verdú (2010) on almost lossless analog compression. The main results of the present paper are a general achievability bound for the compression rate in the analog signal separation problem, an exact expression for the optimal compression rate in the case of signals that have mixed discrete-continuous distributions, and a new technique for showing that the intersection of generic subspaces with subsets of sufficiently small Minkowski dimension is empty. This technique can also be applied to obtain a simplified proof of a key result in Wu and Verdú (2010).

Keywords

Analog signal separation, almost lossless compression, Minkowski dimension

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