Distributed testing against independence with conferencing encoders

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. Due to the restriction of one-shot communication, we consider the distributed testing against independence problem when interaction among the encoders are allowed. Subject to type 1 error probability and communication rates constraints, we first provide a scheme for the general case and then show that this scheme is optimal for some special cases.