Canalizing Boolean Functions Maximize the Mutual Information

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.Comment: Accepted at SCC 2013, Munich, Germany, www.scc2013.ne