In this paper, information theory for studying linear quadratic (LQ) optimal control of linear continuous time invariant systems is developed using control-theoretic approach. In the considered systems, the sensors and the controllers are geographically separated, and connected via digital communication channels carrying a finite number of bits per unit time. Then, the information rates have a dramatic effect on control performance. Under information rate constraints, a control scheme is presented to satisfy given control objectives. In particular, it is shown that, there exist the inherent tradeoffs between the achievable optimal LQ cost and the information rates. A lower bound on the achievable LQ cost is derived for the information rates given. An illustrative example is given to demonstrate the effectiveness of the proposed scheme.