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The problem of a multi-input and multi-output networked control system with communication constraint is addressed in this paper. The shared network medium can only provide a limited number of simultaneous connections for the sensors and actuators to communicate with the controller in the system. A predictive control and scheduling co-design approach is proposed to deal with the problem. In the approach, a predictive controller is applied to generate the predictive control sequences using sensor data and previous control information, and a communication constraint compensator is designed at the actuator side to actively dynamically compensate for the communication constraint in the forward path. The static rate monotonic (RM) scheduling algorithm is considered simultaneously to schedule the transmission of the control signals. Then the co-design scheme is studied. The effectiveness of the proposed results is demonstrated by an illustrative example finally.