In the present paper we obtain the infimal signal-to-noise ratio (SNR) required for the stabilizability of a linear out-put feedback loop over an additive white Gaussian noise (AWGN) channel in closed-form. The focus on AWGN channels allow us to then define the minimal channel capacity required for stabilizability. Finally, the infimal SNR for stabilizability also allow us to identify in closed-form the related stabilizing Hermitian positive semidefinite solution to the continuous-time algebraic Riccati equation of LQ control with vanishing state weight and repeated eigenvalues.