The Weak Simplex Conjecture
Statement
Among equiprobable equal-energy signals in Gaussian noise, is the regular simplex optimal for average error probability? Yes. The underlying comparison is that for any correlation matrix with and , the maximum of the is stochastically dominated by the maximum of independent standard Gaussians.
Context
A named conjecture of long standing in information theory about optimal signal sets under Gaussian noise, with the strong form already known false.
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