Distributed Testing With Interactive Encoders

In this paper, we consider distributed testing problems with interactive encoders, which allow interactive communications among encoders so that each encoder can utilize messages from other encoders for encoding. We first focus on a special case of testing against independence and design a scheme that enables each encoder to take advantage of extra information from other encoders for encoding. We then derive a matching upper bound and prove that the designed scheme is optimal for certain scenarios. We then investigate the case with general hypotheses and obtain a lower bound on the type 2 error exponent. We further compare the performance that can be achieved using interactive communications to that of schemes with non-interactive communications. We show that interactive communication improves the performance in terms of the type 2 error exponent for certain probability mass functions under positive rate communication constraints. On the other hand, we prove that interactive communication does not provide performance gain under zero-rate communication constraints.