The value of feedback for decentralized detection in large sensor networks

We consider the decentralized binary hypothesis testing problem in networks with feedback, where some or all of the sensors have access to compressed summaries of other sensors´ observations. We study certain two-message feedback architectures, in which every sensor sends two messages to a fusion center, with the second message based on full or partial knowledge of the first messages of the other sensors. Under either a Neyman-Pearson or a Bayesian formulation, we show that the asymptotically optimal (in the limit of a large number of sensors) detection performance (as quantified by error exponents) does not benefit from the feedback messages.