ERROR EXPONENTS FOR DISTRIBUTED DETECTION OF MARKOV SOURCES

The paper considers a binary hypothesis testing system in which two se nsors simultaneously observe a discrete-time finite-valued stationary ergodic Markov source and transmit M-ary messages to a Neyman-Pearson central detector. The size M of the message alphabet increases at most subexponentially with the number of observations. The asymptotic beha vior of the type II error rate is investigated as the number of observ ations increases to infinity, and the associated error exponent is obt ained under mild assumptions on the source distributions. This exponen t is independent of the test level epsilon and the actual codebook siz es M, is achieved by a universally optimal sequence of acceptance regi ons, and is characterized by an infimum of informational divergence ra te over a class of infinite-dimensional distributions. Important diffe rences-due to the observations being Markov-between the asymptotically optimal distributed tests and their nondistributed counterparts are h ighlighted. The converse results require a blowing-up lemma for statio nary ergodic Markov sources, which is also proven.