Exact Rate Exponent Tradeoff for New Classes of Distributed Hypothesis Testing Problems
2026-08-24 • Information Theory
Information Theory
AI summaryⓘ
The authors studied how well two parties can test between two hypotheses when one party can only send limited information to the other. They focused on a specific kind of test called one-way distributed hypothesis testing and found the exact relationship between communication rate and error probability. By simplifying an upper bound, they showed it matches known lower bounds, proving the bound is exact in some cases. They confirmed this exact characterization for certain binary sources with specific noise levels, regardless of how much data is sent.
distributed hypothesis testingtype-II error exponentrate-exponent tradeoffauxiliary-receiver techniqueone-way communicationtesting against dependencedoubly symmetric binary sourcecrossover probabilitynull hypothesisalternative hypothesis
Authors
Zhenduo Wen, Amin Gohari, Michèle Wigger
Abstract
We characterize the exact rate--exponent tradeoff for new classes of one-way distributed hypothesis testing problems by demonstrating that a recent upper bound, derived via the auxiliary-receiver technique, coincides with known lower bounds. We achieve this by relaxing the upper bound on the type-II error exponent into a form that shares the same inner functional as Han's lower bound, differing only in the outer rate constraint. Furthermore, we prove that this upper bound is tight for testing against dependence and for the doubly symmetric binary source (DSBS) with crossover probabilities $κ_0$ under the null hypothesis and $κ_1$ under the alternative hypothesis, provided $0 < κ_1 \leq κ_0 < \frac12$. The characterization of the exact error exponent for the DSBS source holds for every communication rate $R \geq 0$.