Sensing and communication with and without bits

The successful design of sensor network architectures depends crucially on the structure of the sampling, observation, and communication processes. One of the most fundamental ques- tions concerns the sufficiency of discrete approximations in time, space, and amplitude. In the case of space and time, the question can be rephrased as whether there is a spatio- temporal sampling theorem for typical data sets in sensor net- works. This question has a positive answer in many cases of interest. The issue of discretization of amplitudes is more subtle and can be expressed as the question of whether there is a (source/channel) separation theorem for typical sensor networks. We show that this question has a negative answer in general and that the price of separation can be large. To illustrate these issues, we review the underlying theory and discuss specific examples.