Simple local partition rules in multi-bit decision fusion

A parallel decision fusion system is studied where local detectors (LDs) collect information about a binary hypothesis, and transmit multi-bit intermediate decisions to a data fusion center (DFC). The DFC compresses the local decisions into a final binary decision. The objective function is the Bayesian risk. Equations for the optimal decision rules for the LDs and the DFC have been derived by Lee-Chao (1989), but the computational complexity of solving them is formidable. To address this difficulty, we propose several suboptimal LD-design schemes. For each one we design a DFC, which is optimally conditioned on the fixed LD rules. We calculate the exact performance of each scheme, thus providing a means for selection of the most appropriate one under given observation conditions. We demonstrate performance for two important binary decision tasks: discrimination between two Gaussian hypotheses of equal variances and different means; and discrimination between two Gaussian hypotheses of equal means and different variances