A Tight Upper Bound on the Mutual Information of Two Boolean Functions
Georg Pichler, Gerald Matz, Pablo Piantanida · 2016
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.