Two-Hop Network with Multiple Decision Centers under Expected-Rate Constraints.

The paper studies distributed binary hypothesis testing over a two-hop relay network where both the relay and the receiver decide on the hypothesis. Both communication links are subject to \emph{expected} rate constraints, which differs from the classical assumption of maximum rate constraints. We exactly characterize the set of type-II error exponent pairs at the relay and the receiver when both type-I error probabilities are constrained by the same value $\epsilon>0$. No tradeoff is observed between the two exponents, i.e., one can simultaneously attain maximum type-II error exponents both at the relay and at the receiver. For $\epsilon_1 \neq \epsilon_2$, we present an achievable exponents region, which we obtain with a scheme that applies different versions of a basic two-hop scheme that is optimal under \emph{maximum} rate constraints. We use the basic two-hop scheme with two choices of parameters and rates, depending on the transmitter's observed sequence. For $\epsilon_1=\epsilon_2$, a single choice is shown to be sufficient. Numerical simulations indicate that extending to three or more parameter choices is never beneficial.