Distributed testing with zero-rate compression

Motivated by distributed inference over big datasets problems, we study multi-terminal distributed hypothesis testing problems in which each terminal has data related to only one random variable. We consider a case of practical interest in which each terminal is allowed to send zero-rate messages to a decision maker. Subject to a constraint that the error exponent of the type 1 error probability is larger than a certain level, we characterize the best error exponent of the type 2 error probability using basic properties of the r-divergent sequences.