Distributed Detection with Feedback

Abstract

We investigated the effects of feedback on a decentralized detection system consisting of N sensors and a data fusion center. It is assumed that observations are independent and identically distributed across sensors, and that each sensor uses a randomized scheme for compressing its observations into a fixed number of quantization levels. We consider two variations on this setup. One entails the transmission of sensor data to the fusion center in two stages, and the broadcast of feedback information from the center to the sensors after the first stage. The other variation involves information exchange between sensors prior to transmission to the fusion center; this exchange is effected through a feedback decision center, which processes binary data from the sensors and thereafter broadcasts a single feedback bit back to the sensors. We show that under the Neyman- Pearson criterion, only the latter type of feedback yields an improvement on the asymptotic performance of the system (as N ƀ ), and we derive the associated error exponents. We also demonstrate that deterministic compression schemes are asymptotically as powerful as randomized ones