We deal with the stabilization problem for a class of nonlinear discrete-time systems via a digital communication channel. We consider the case when the control input is to be transmitted via communication channels with a bit-rate constraint. Under an appropriate growth condition on the nonlinear perturbation, we establish sufficient conditions for the global and local stabilizability of semilinear and nonlinear discrete-time systems, respectively. A constructive method to design a feedback stabilizing controller is proposed.