This paper studies control problems for discrete-time single-input linear time-invariant plants when controlled over a signal-to-noise ratio (SNR) constrained channel. Our focus is on the performance limitations in an architecture that uses channel feedback. We explicitly characterize the interplay between stabilization, optimal performance, and SNR constraints, highlighting the way in which plant dynamical features affect the best achievable performance. We also apply our results to the study of networked control systems where communication takes place over a power constrained erasure channel. In that scenario, we first show that stabilization problems, and problems involving stationary secondorder moments, can be dealt with by focusing on a related SNR constrained networked situation. This observation allows one to obtain results valid in the alternative scenario as corollaries of the results obtained when a single SNR constraint is present. (C) 2012 Elsevier Ltd. All rights reserved.