This paper studies the communication rate requirements for state estimation in a remote control setting where the controller and the plant are connected through communication links, such as the Internet. Such links introduce random delays and occasional packet losses in the transmission of information, which along with quantization and sampling lead to deterioration of control performance. One controlled element here is the rate of quantization, which has a direct effect on the control performance. In this paper, the rate required for the stability of the differential entropy of the state estimation error is determined as a function of the system and network parameters. The trade-off between the sampling period, packet loss probability and the rate requirements is illustrated. A Markov chain model is introduced to capture the state of reliability of the network. Conditions for stability in mean in a control theoretic setting are studied.