Quantizer Precision for Distributed Estimation in a Large Sensor Network

We investigate the design of simple noncooperative quantizers for distributed estimation of a common random variable. It is assumed that there is a budget of aggregate rate, a criterion of Fisher information, and a large population of sensors. It is further assumed that sensor quantizers are uniform, and that rate is determined by the entropy of the outputs of these. The key question asked is whether it is better to quantize a relatively few sensors finely or as many as possible coarsely