Error exponents for distributed detection of Markov sources

The paper considers a binary hypothesis testing system in which two sensors 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 behavior of the type II error rate is investigated as the number of observations increases to infinity, and the associated error exponent is obtained under mild assumptions on the source distributions. This exponent is independent of the test level ε and the actual codebook sizes M, is achieved by a universally optimal sequence of acceptance regions, and is characterized by an infimum of informational divergence rate over a class of infinite-dimensional distributions. Important differences-due to the observations being Markov-between the asymptotically optimal distributed tests and their nondistributed counterparts are highlighted. The converse results require a blowing-up lemma for stationary ergodic Markov sources, which is also proven