We study sensor networks where the fusion center wants to recover a function of the underlying sources, perhaps to within some distortion.
The sensors observe noisy versions of the underlying sources and communicate to the fusion center subject to interference and noise. What are the right architectural guidelines?
Conventional wisdom suggests a modular design where the sensors compress their observations into a bit stream and communicate that bit stream to the fusion center using error control codes, which we will refer to as "digital communication." In this perspective, bits are the universal currency of information.
We have shown that in some cases, this leads to exponentially suboptimal performance (in the number of sensor required to attain a prescribed level of fidelity), showing that bits are not a fundamental universal currency of information in networks.
This begs several questions. The most immediate is: what subclass of sensor network problems can be addressed via bits (digital communication) without a catastrophic loss of optimality? We discuss the state of the art on this question, and then show a class of counterexamples, including the problem of reliable computation in sensor network scenarios, for which digital communication is the wrong architecture.
At a more fundamental level, the question is how to order sensor network problems according to their difficulty. Whenever digital communication is optimal, this ordering can be achieved in terms of bits (capacities and rate-distortion functions). However, when digital communication is exponentially suboptimal, different abstractions are necessary.
We discuss some approaches to this.
This is, in part, joint work with Martin Vetterli, Anand Sarwate, Bobak Nazer, and Pier Luigi Dragotti.