One-Shot Achievability Region for Hypothesis Testing with Communication Constraint

Yuanxin Guo, Sadaf Salehkalaibar, Stark C. Draper, Wei Yu

Abstract: The paper considers a communication constrained distributed hypothesis testing problem in which the transmitter sends a message about its local observation to the receiver, and the receiver tries to decide whether or not its own observation is independent of the observation at the transmitter. We analyze the problem in the one-shot setting and derive an achievability region under both the fixed-length and the variable-length communication constraints. Novel information-theoretic tools, including the generalized Poisson matching lemma and the strong functional representation lemma, are applied. It is shown that the proposed one-shot schemes, when applied to the asymptotic case, recover the optimal fixed-length and variable-length type-II error exponents for testing against independence.