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A Tight Upper Bound on the Mutual Information of Two Boolean Functions

Georg Pichler (TU Wien), Gerald Matz (TU Wien), Pablo Piantanida (Université Paris-Sud, Centre National de la Recherche Scientifique)

IEEE Information Theory Workshop (ITW)

DOI: 10.1109/itw.2016.7606787 (Mathematics)

Abstract: Let (X,Y) be a doubly symmetric binary source. For n i.i.d. copies (Xn,Yn) of (X,Y) we show that max[I(f(Xn); g(Yn))]= I(X,Y), where the maximum is over all Boolean functions f, g: {0, 1}n→ {0, 1}. This positively resolves a conjecture published by Kumar and Courtade in 2013.

Published on 01 Sep. 2016