We study a closed-loop control system with feedback transmitted over a noisy discrete memoryless channel. We design encoder-controller pairs that jointly optimize the sensor measurement quantization, protection against channel errors, and control. The designgoal is to minimize an expected linear quadratic cost over a finite horizon. As a result of deriving optimality criteria for this problem, we present new results on the validity of theseparation principle subject to certain assumptions. More precisely, we show that the certainty equivalence controller is optimal when the encoder is optimal and has full side-information about the symbols received at the controller. We then use this result to formulate tractable design criteria in the general case. Finally, numerical experiments are carried out to demonstrate the performance obtained by various design methods.