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Entropy 2016, 18(11), 410; doi:10.3390/e18110410

Information-Theoretic Analysis of Memoryless Deterministic Systems

1
Institute for Communications Engineering, Technical University of Munich, Munich 80290, Germany
2
Signal Processing and Speech Communication Laboratory, Graz University of Technology, Graz 8010, Austria
*
Author to whom correspondence should be addressed.
Academic Editors: Raúl Alcaraz Martínez and Kevin H. Knuth
Received: 18 August 2016 / Revised: 27 October 2016 / Accepted: 14 November 2016 / Published: 17 November 2016
(This article belongs to the Section Information Theory)
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Abstract

The information loss in deterministic, memoryless systems is investigated by evaluating the conditional entropy of the input random variable given the output random variable. It is shown that for a large class of systems the information loss is finite, even if the input has a continuous distribution. For systems with infinite information loss, a relative measure is defined and shown to be related to Rényi information dimension. As deterministic signal processing can only destroy information, it is important to know how this information loss affects the solution of inverse problems. Hence, we connect the probability of perfectly reconstructing the input to the information lost in the system via Fano-type bounds. The theoretical results are illustrated by example systems commonly used in discrete-time, nonlinear signal processing and communications. View Full-Text
Keywords: information processing; signal processing; system theory; Fano’s inequality; information loss; Rényi information dimension information processing; signal processing; system theory; Fano’s inequality; information loss; Rényi information dimension
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Geiger, B.C.; Kubin, G. Information-Theoretic Analysis of Memoryless Deterministic Systems. Entropy 2016, 18, 410.

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