Preprint
Sep 2026
A Proof of the Most Informative Boolean Function Conjecture
Let $X$ be uniform on $\{-1,1\}^n$, let $Y$ be obtained by passing its coordinates independently through a binary symmetric channel with crossover probability $p$, and let $g:\{-1,1\}^n\to\{0,1\}$ be a Boolean function. We give a computer-assisted proof of the Courtade--Kumar conjecture $I(g(X);Y)\le1-H_2(p)$, where $H...
Zi-Jie Chen, Amin Gohari, Adel Javanmard et al.
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