Distributed Hypothesis Testing with Variable-Length Coding

This paper characterizes the optimal type-II error exponent for a distributed hypothesis testing-against-independence problem when the expected rate of the sensor-detector link is constrained. Unlike for the well-known Ahlswede-Csiszar result that holds under a maximum rate constraint and where a strong converse holds, here the optimal exponent depends on the allowed type-I error exponent. Specifically, if the type-I error probability is limited by ε, then the optimal type-II error exponent under an expected rate constraint R coincides with the optimal type-II error exponent under a maximum rate constraint of (1 - ε)R.