Distributed Testing With Cascaded Encoders

摘要

In this paper, we consider distributed testing problems with cascaded encoders, which allow cascaded 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. We also derive a matching upper bound and prove that the designed scheme is optimal. We then investigate the case with general hypotheses and obtain a lower bound on the type 2 error exponent. We further compare the performances that can be achieved by schemes with and without cascaded communications. We show that cascaded communication improves the performance in terms of the type 2 error exponent under positive rate communication constraints. On the other hand, we prove that cascaded communication does not provide performance gain under zero-rate communication constraints.