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We study a hypothesis testing problem in which data is compresseddistributively and sent to a detector that seeks to decide between two possibledistributions for the data. The aim is to characterize all achievable encodingrates and exponents of the type 2 error probability when the type 1 errorprobability is at most a fixed value. For related problems in distributedsource coding, schemes based on random binning perform well and often optimal.For distributed hypothesis testing, however, the use of binning is hindered bythe fact that the overall error probability may be dominated by errors inbinning process. We show that despite this complication, binning is optimal fora class of problems in which the goal is to "test against conditionalindependence." We then use this optimality result to give an outer bound for amore general class of instances of the problem.

Optimality of Binning for Distributed Hypothesis Testing