This paper investigates quantized feedback stabilization problems for discretetime linear time-invariant systems over noisy, bandwidth-limited digital communication channels. The packet dropout process of the channel is modeled as a Markov process. In particular, the case with limited data rates is considered. An observer-based control and quantization scheme is presented. A sufficient condition on the data rate for stabilization of the MIMO system is derived. An illustrative example is given to demonstrate the effectiveness of the proposed method.