Operational Equivalence of Distributed Hypothesis Testing and Identification Systems

Abstract

In this paper we revisit the connections of the distributed hypothesis testing against independence (HT) problem with the Wyner-Ahlswede-Körner (WAK) problem and the identification systems (ID). We show that the strong converse for the WAK problem is equivalent to the strong converse for the HT problem via constructive and nonconstructive transformations of codes. As another consequence of the transformation we provide a new exponentially strong converse equivalence statement. Applying the same idea, we prove a new result that the-identification capacity of the ID problem is equal to the maximum-exponent of type II of error in the HT problem when both side compression is allowed.