We present an event-triggered controller for stabilizing a continuous-time linear time-invariant system subject to communication constraints. We model the communication constraints as a noiseless finite-capacity communication channel between the process sensors and the controller/actuator. An encoder converts the process state into symbols to send across the channel to the controller/actuator, which converts the symbols into a state estimate to be used in a simple emulation-based state-feedback control law. We derive a sufficient condition for this scheme to stabilize the process. The condition depends on the encoder's average bit-rate, its average consumption of communication resources, and the eigenvalues of the process. The proposed encoding scheme is order-optimal in the sense that its stability condition is within a constant factor of the optimal bound from previous work.