Distributed identity testing with zero-rate compression

Wenwen Zhao, Lifeng Lai

Abstract: In this paper, we consider the identity testing problems in the distributed setting, in which each terminal has data only relates to one random variable. Each terminal sends zero-rate message to the decision maker, and the decision maker decides the distribution of (X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , Y <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ), which is indirectly revealed from the encoded messages, is the same as or λ-far from a given distribution. Interpreting this as a distributed composite hypothesis testing problem, we characterize the best error exponent of the type 2 error probability using a universal coding scheme under the exponential-type constraint on the type 1 error probability.