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

TL;DR

This paper characterizes the error exponents in a two-hop distributed hypothesis testing network under expected rate constraints, revealing no tradeoff between relay and receiver error exponents and proposing an optimal scheme.

Contribution

It provides an exact characterization of error exponents under expected rate constraints and introduces a scheme that achieves these exponents, extending classical maximum rate results.

Findings

Maximum error exponents are simultaneously attainable at relay and receiver.

A simple two-parameter scheme suffices for optimal performance.

Extending to more parameters does not improve the exponents.

Abstract

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 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 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.