Asymptotic Optimality Theory for Decentralized Sequential Hypothesis Testing in Sensor Networks

The decentralized sequential hypothesis testing problem is studied in sensor networks, where a set of sensors receive independent observations and send summary messages to the fusion center, which makes a final decision. In the scenario where the sensors have full access to their past observations, the first asymptotically Bayes sequential test is developed having the same asymptotic performance as the optimal centralized test that has access to all sensor observations. Next, in the scenario where the sensors do not have full access to their past observations, a simple but asymptotically Bayes sequential tests is developed, in which sensor message functions are what we call tandem quantizer, where each sensor only uses two different sensor quantizers with at most one switch between these two possibilities. Moreover, a new minimax formulation of optimal stationary sensor quantizers is proposed and is studied in detail in the case of additive Gaussian sensor noise. Finally, our results show that in the simplest models, feedback from the fusion center does not improve asymptotic performance in the scenario with full local memory, however, even a one-shot, one-bit feedback can significantly improve performance in the case of limited local memory.