Polynomial-Time MIMO Detection at the Maximum-Likelihood Threshold

We prove that exact block recovery in the square Gaussian binary MIMO model can be achieved in polynomial time at the same first-order SNR threshold as exhaustive maximum-likelihood detection. Specifically, for $y=\sqrt{ρ/N}Hx^\star+w, \; x^\star\in\{\pm1\}^N,$ and independent standard Gaussian $H\i