There is an increasing interest in studying control systems employing multiple sensors and actuators that are geographically distributed. Communication is an important component of these distributed and networked control systems. Hence, there is a need to understand the interactions between the control components and the communication components of the distributed system. In this paper, we formulate a control problem with a communication channel connecting the sensor to the controller. Our task involves designing the channel encoder and channel decoder along with the controller to achieve different control objectives. We provide upper and lower bounds on the channel rate required to achieve these different control objectives. In many cases, these bounds are tight. In doing so, we characterize the "information complexity" of different control objectives.