For Gaussian one-bit measurements, the correlation of any convex-loss estimator is sharply predicted by a system of three equations, yielding new per-estimator comparisons and an optimality bound.
Log-Quadratic Bounds for the Gaussian Q-function
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abstract
We present bounds of quadratic form for the logarithm of the Gaussian Q-function. We also show an analytical method for deriving log-quadratic approximations of the Q-function and give an approximation with absolute error less than $10^{-3}$.
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Sharp Guarantees for Solving Random Equations with One-Bit Information
For Gaussian one-bit measurements, the correlation of any convex-loss estimator is sharply predicted by a system of three equations, yielding new per-estimator comparisons and an optimality bound.