This paper considers Cyber-Physical Systems (CPSs) in the presence of Denial-of-Service (DoS) attacks, and investigates the networked control problem under data rate limitations. We develop a framework for CPSs in the presence of DoS attacks, and present a state-estimate control scheme for CPSs under DoS attacks. For the different communication status, the information on the plant state is transmitted to the controller by employing a different data rate in order to mitigate the influence of DoS attacks. Sufficient conditions on the data rate for mean square observability and stabilization of CPSs are derived by applying information theoretic tools of source coding. Our result is less conservative than some existing results. An illustrative example is given to demonstrate the effectiveness of the proposed quantization-coding scheme.