Error Exponents for Distributed Detection with Feedback'

We investigate the effects of feedback on a decentralized detection system consisting of N sensors and a detection center. It is assumed that observations are independent and identically distributed across sensors, and that each sensor compresses 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, with 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 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 results in an improvement in the asymptotic performance of the system (as N -+ CO) and we derive the associated error exponents.