Communication is an important component of distributed and networked controls systems. In our companion paper, we presented a framework for studying control problems with a digital noiseless communication channel connecting the sensor to the controller. Here, we generalize that framework by applying traditional information theoretic tools of source coding and channel coding to the problem. We present a general necessary condition for observability and stabilizability for a large class of communication channels. Then, we study sufficiency conditions for Internet-like channels that suffer erasures.