Theoretical Bounds in Decentralized Hypothesis Testing

Three fundamental problems are addressed for distributed detection networks regarding the maximum of performance/detection loss. The losses obtained are, first, due to the choice of decision rule in parallel sensor networks (general-case vs identical decisions), second, due to the choice of network architecture (serial vs parallel), and third, due to the choice of quantization rule (centralized vs decentralized). Previous results, if available, for all these three problems are restricted to the statement that the loss is "small" over some specific examples. The key principles underlying this study are delineated as follows. First, there is a surjection from all simple hypothesis tests to the receiver operating characteristic (ROC) curve. Second, the ROC can be well modeled with linear splines. Third, considering splines with only a finite number of line segments, in fact, on the order of the total number of sensors, is sufficient to determine the maximum loss. Leveraging these principles, infinite-dimensional optimization problems are reduced to their finite-dimensional equivalent forms. The equivalent problems are then numerically solved to obtain the theoretical bounds.