Or Ordentlich, Ofer Shayevitz, Omri Weinstein

Suppose $X$ is a uniformly distributed $n$-dimensional binary vector and $Y$ is obtained by passing $X$ through a binary symmetric channel with crossover probability $\alpha$. A recent conjecture by Courtade and Kumar postulates that $I(f(X);Y)\leq 1-h(\alpha)$ for any Boolean function $f$. In this paper, we prove the conjecture for all ... more >>>