For a binary channel on a uniform discrete cube under independent symmetric noise, a noisy coordinate maximizes retained information at fixed initial information; for Boolean functions this gives I(f(X);Y) ≤ 1 − h₂(ε) at crossover probability 0≤ε≤1/2.
For a binary channel on a uniform discrete cube under independent symmetric noise, a noisy coordinate maximizes retained information at fixed initial information; for Boolean functions this gives I(f(X);Y) ≤ 1 − h₂(ε) at crossover probability 0≤ε≤1/2.
For a binary channel on a uniform discrete cube under independent symmetric noise, a noisy coordinate maximizes retained information at fixed initial information; for Boolean functions this gives I(f(X);Y) ≤ 1 − h₂(ε) at crossover probability 0≤ε≤1/2.
If correct, resolves the Courtade–Kumar conjecture for all Boolean functions and noise levels, with a sharper output-bias refinement.
Does a noisy coordinate maximize retained binary information on the uniform discrete cube?
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OpenAI reports sharp binary-information contraction on the discrete cube
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