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Suppose $Y^{n}$ is obtained by observing a uniform Bernoulli random vector $X^{n}$ through a binary symmetric channel. Courtade and Kumar asked how large the mutual information between $Y^{n}$ and a Boolean function $ \mathsf {b}(X^{n})$ could be, and conjectured that the maximum is attained by a dictator function. An equivalent formulation of this conjecture is that dictator minimizes the...
Suppose Y n is obtained by observing a uniform Bernoulli random vector Xn through a binary symmetric channel. Courtade and Kumar asked how large the mutual information between Y n and a Boolean function b(Xn) could be, and conjectured that the maximum is attained by the dictator function. An equivalent formulation of this conjecture is that dictator minimizes the prediction cost in sequentially predicting...
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