Distributed M-ary hypothesis testing with binary local decisions

Parallel distributed detection schemes for M-ary hypothesis testing often assume that for each observation the local detector transmits at least log ₂M bits to a data fusion center (DFC). However, it is possible for less than log₂M bits to be available, and in this study we consider 1-bit local detectors with M>2. We develop conditions for asymptotic detection of the correct hypothesis by the DFC, formulate the optimal decision rules for the DFC, and derive expressions for the performance of the system. Local detector design is demonstrated in examples, using genetic algorithm search for local decision thresholds. We also provide an intuitive geometric interpretation for the partitioning of the observations into decision regions. The interpretation is presented in terms of the joint probability of the local decisions and the hypotheses.