This paper addresses linear quadratic Gaussian (LQG) control problems for multi-input multioutput (MIMO), linear time-invariant (LTI) systems, where the sensors and controllers are geographically separated and connected via a digital communication channel with limited data rates. An observer-based, quantized state feedback control scheme is employed in order to achieve the minimum data rate for mean square stabilization of the unstable plant. An explicit expression is presented to state the tradeoff between the LQ cost and the data rate. Sufficient conditions on the data rate for mean square stabilization are derived. An illustrative example is given to demonstrate the effectiveness of the proposed scheme.