On multi-level decentralized binary detection in sensor networks

In this paper, we study multi-level decentralized binary detection in clustered sensor networks from a joint communication/information-theoretic perspective. The starting point is a Bayesian approach for the minimization of the probability of decision error. We consider sensor networks with uniform clustering, a generic number of intermediate information fusion centers (FCs), and noisy communication links. In particular, noisy communication links are modeled as binary symmetric channels (BSCs). Our results show that the performance, in terms of probability of decision error, with uniform clustering depends only on the number of decision levels, but not on the particular clustering configuration. The proposed communication-theoretic approach is then extended to the information-theoretic realm, using the concept of mutual information of the sensor network. The two approaches are then combined in a joint communication/information-theoretic framework. We show that, for a given value of the network mutual information, the probability of decision error is uniquely determined. Finally, we derive a simplified model for the information-theoretic analysis and we show that it predicts accurately the exact network performance. Based on this model, we find simple relationships between the probability of decision error and the mutual information. The results predicted by the analytical framework are confirmed by simulations.