Distributed testing against independence with multiple terminals

Motivated by distributed learning with Big Data sets problems, we study a distributed testing against independence problem with multiple terminals. We connect the problem at hand to a source coding with multiple helpers problem, which is open in general. We fully characterize the rate region of the source coding with multiple helpers problem under a certain Markovian condition. Using this rate region characterization, we obtain a single-letter characterization of the optimal error exponent for the type 2 error probability under the type 1 error probability and communication rates constraints.