This paper focuses on LQ (linear quadratic) control of MIMO (multi-input multi-output), discrete-time linear systems, where the sensors and the controller are connected via a digital communication channel with limited data rates. In particular, it is shown that there exists the inherent tradeoffs between LQ cost and data rates. The data rate has important effects on the optimal quadratic cost. An upper bound on the achievable performance is derived for the data rate given. An illustrative example is given to demonstrate the effectiveness of the proposed method.