Hypothesis Testing and Identification Systems

We study hypothesis testing problems with fixed compression mappings and with user-dependent compression mappings to decide whether or not an observation sequence is related to one of the users in a database, which contains compressed versions of previously enrolled users' data. We first provide the optimal characterization of the exponent of the probability of the second type of error for the fixed compression mappings scenario when the number of users in the database grows exponentially. We then establish operational equivalence relations between the Wyner-Ahlswede-Körner network, the single-user hypothesis testing problem, the multi-user hypothesis testing problem with user-dependent compression mappings and the identification systems with user-dependent compression mappings. These equivalence relations imply the strong converse and exponentially strong converse for the multi-user hypothesis testing and the identification systems both with user-dependent compression mappings. Finally they also show how an identification scheme can be turned into a multi-user hypothesis testing scheme with an explicit transfer of rate and error probability conditions and vice versa.