The research area of control over networks has attracted great interest in recent years. Inserted in this research area is the study of control feedback limitations imposed by the presence of a communication channel. In this paper we analyze the fundamental limitations in control feedback stabilizability imposed by a class of Signal-to-Noise Ratio (SNR) constrained communication channels. We solve the SNR constrained control over network problem as a linear quadratic Gaussian (LQG) optimization with loop transfer recovery (LTR). If the communication channel is located on the feedback path then the LTR is said to be performed at the output. Vice versa, if the communication channel is on the control path, then the recovery is said to be performed at the input. In the present paper we address both cases, namely the LQG optimization with LTR at the output and the LQG optimization with LTR at the input to solve an LTI SNR constrained problem. We then explore the link between these two solutions.