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Distributed Hypothesis Testing with Variable-Length Coding (1910.08261v1)
Published 18 Oct 2019 in cs.IT and math.IT
Abstract: This paper characterizes the optimal type-II error exponent for a distributed hypothesis testing-against-independence problem when the \emph{expected} rate of the sensor-detector link is constrained. Unlike for the well-known Ahlswede-Csiszar result that holds under a \emph{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 $\epsilon$, then the optimal type-II error exponent under an \emph{expected} rate constraint $R$ coincides with the optimal type-II error exponent under a \emph{maximum} rate constraint of $(1-\epsilon)R$.