Canalizing Boolean Functions Maximize the Mutual Information

Conference: SCC 2013 - 9th International ITG Conference on Systems, Communication and Coding
01/21/2013 - 01/24/2013 at München, Deutschland

Proceedings: SCC 2013

Pages: 6Language: englishTyp: PDF

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Klotz, Johannes Georg; Kracht, David; Bossert, Martin; Schober, Steffen (Institute of Communications Engineering, Ulm University, Albert-Einstein-Allee 43, 89073 Ulm, Germany)

The ability of information processing in biologically motivated Boolean networks is of interest in recent information theoretic research. One measure to quantify this ability is the well known mutual information. Using Fourier analysis we show that canalizing functions maximize the mutual information between an input variable and the outcome of the function. We proof our result for Boolean functions with uniform distributed as well as product distributed input variables.