Title :
CommentsComments on “Canalizing Boolean Functions Maximize Mutual Information”
Author :
Courtade, Thomas A.
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Univ. of California at Berkeley, Berkeley, CA, USA
Abstract :
In their recent paper “Canalizing Boolean Functions Maximize Mutual Information,” Klotz et al. argued that canalizing Boolean functions maximize certain mutual informations by an argument involving Fourier analysis on the hypercube. This note supplies short new proofs of their results based on a coupling argument and also clarifies a point on the necessity of considering randomized functions.
Keywords :
Boolean functions; Fourier analysis; Fourier analysis; canalizing Boolean functions; coupling argument; hypercube; mutual information; randomized functions; Boolean functions; Couplings; Data processing; Irrigation; Joints; Mutual information; Random variables; Boolean functions; Mutual Information; mutual information;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2014.2375183
