  We study the performance of a wide class of convex optimization-based
estimators for recovering a signal from corrupted one-bit measurements in
high-dimensions. Our general result predicts sharply the performance of such
estimators in the linear asymptotic regime when the measurement vectors have
entries IID Gaussian. This includes, as a special case, the previously studied
least-squares estimator and various novel results for other popular estimators
such as least-absolute deviations, hinge-loss and logistic-loss. Importantly,
we exploit the fact that our analysis holds for generic convex loss functions
to prove a bound on the best achievable performance across the entire class of
estimators. Numerical simulations corroborate our theoretical findings and
suggest they are accurate even for relatively small problem dimensions.
