Tight upper bound on the mutual information of two boolean functions

Pichler Georg , Pablo Piantanida (1) , Gerald Matz (2)

1 L2S - Laboratoire des signaux et systèmes
2 Institute for Telecommunications, Vienna University of Technology (Vienna University)

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.

Domaines: Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]; Statistiques [math.ST]

Pichler Georg, Pablo Piantanida, Gerald Matz. Tight upper bound on the mutual information of two boolean functions. 2016 IEEE Information Theory Workshop (ITW), Sep 2016, cambridge, United Kingdom. ⟨10.1109/ITW.2016.7606787⟩. ⟨hal-01436893⟩