Almost Lossless Analog Signal Separation

TL;DR

This paper introduces an information-theoretic approach to analog signal separation, providing bounds on compression rates and new techniques for analyzing subspace intersections, extending prior work on analog compression.

Contribution

It offers a general achievability bound for compression rates in analog separation and derives an exact rate for signals with mixed distributions, along with a novel intersection technique.

Findings

Established a bound for compression rate in analog separation.

Derived exact compression rate for mixed discrete-continuous signals.

Introduced a new method for analyzing subspace intersections with small Minkowski dimension.

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 Verd\'u (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 Verd\'u (2010).