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Information Loss in Static Nonlinearities

By Bernhard C. Geiger, Christian Feldbauer and Gernot Kubin

Abstract

In this work, conditional entropy is used to quantify the information loss induced by passing a continuous random variable through a memoryless nonlinear input-output system. We derive an expression for the information loss depending on the input density and the nonlinearity and show that the result is strongly related to the non-injectivity of the considered system. Tight upper bounds are presented, which can be evaluated with less difficulty than a direct evaluation of the information loss, which involves the logarithm of a sum. Application of our results is illustrated on a set of examples.Comment: 9 pages, 6 figures; A short version of this paper is submitted to an IEEE conferenc

Topics: Computer Science - Information Theory, Nonlinear Sciences - Exactly Solvable and Integrable Systems
Year: 2011
DOI identifier: 10.1109/ISWCS.2011.6125272
OAI identifier: oai:arXiv.org:1102.4794
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