This paper presents a control system design strategy for multivariable plants where the controller, sensors and actuators are connected via a digital, data-rate limited, communications channel. In order to minimize bandwidth utilization, a communication constraint is imposed which restricts all transmitted data to belong to a finite set and only permits one plant to be addressed at a time. We emphasize implementation issues and employ moving horizon techniques to deal with both control and measurement quantization issues. We illustrate the methodology by simulations and a laboratory-based pilot-scale study.