Interactive hypothesis testing with communication constraints

Abstract—This paper studies the problem of interactive hypothesis testing with communication constraints, in which two communication nodes separately observe one of two correlated sources and interact with each other to decide between two hypotheses on the joint distribution of the sources. When testing against independence, that is, the joint distribution of the sources under the alternative hypothesis is the product of the marginal distributions under the null hypothesis, a computable characterization is provided for the optimal tradeoff between the communication rates in two-round interaction and the testing performance measured by the type II error exponent such that the type I error probability asymptotically vanishes. An example is provided to show that interaction is strictly helpful. I