In this paper we address the problem of finding a stabilizing feedback controller for a linear time invariant (LTI) plant model when measurement is performed over a communication channel model subject to channel input logarithmic quantization and a signal-to-noise ratio (SNR) constraint. The location of the communication channel is therefore on the measurement path, that is between the plant and the controller, nevertheless similar results can be obtained for the alternative location over the control path. In our first approach the communication channel model itself is selected to be an additive white Gaussian noise (AWGN) channel. We then describe the spectral power density of the channel density as a function of the power spectral density of the channel additive white Gaussian noise and the uniform distributed process model arising from a logarithmic quantization. The infimal channel SNR is then obtained through the definition for the channel input power, together with an interpretation of a bound on the logarithmic quantization relative error as a multiplicative modeling error. In our second approach we extend the proposed analysis to the class of additive colored Gaussian noise (ACGN) channels with memory. The infimal SNR is then obtained again through the definition for the channel input power. Finally, an extension to the case of sampled-data systems is proposed. © 2011 IFAC.