Exact Rate Exponent Tradeoff for New Classes of Distributed Hypothesis Testing Problems
Abstract
We study the optimal Stein error exponent for one-way distributed hypothesis testing under a communication rate constraint. We establish exact rate-exponent tradeoffs for new classes of finite-alphabet sources, including a complete single-letter characterization for every pair of strictly positive binary joint distributions as well as testing-against-dependence. Our converse analysis refines the auxiliary-receiver method through three complementary steps. First, we establish an information-projection identity that identifies the posterior-divergence optimization in an existing converse with Han's exponent functional. Second, we obtain an additional excess-rate branch by retaining a mutual-information term discarded in the usual rate relaxation. Third, we develop a two-telescope upper bound whose auxiliary variables are coupled through a joint rate constraint. Combining these bounds with information-geometric matching conditions yields exact exponents for three classes of sources by matching the achievable bounds of Han and Shimokawa-Han-Amari.
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BibTeX
@misc{wen2026exact,
title = {{Exact Rate Exponent Tradeoff for New Classes of Distributed Hypothesis Testing Problems}},
author = {Zhenduo Wen and Amin Gohari and Michèle Wigger},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.23465},
eprint = {2608.23465},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.23465},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Exact Rate Exponent Tradeoff for New Classes of Distributed Hypothesis Testing Problems
AU - Zhenduo Wen
AU - Amin Gohari
AU - Michèle Wigger
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2608.23465
UR - https://arxiv.org/abs/2608.23465
AB - We study the optimal Stein error exponent for one-way distributed hypothesis testing under a communication rate constraint. We establish exact rate-exponent tradeoffs for new classes of finite-alphabet sources, including a complete single-letter characterization for every pair of strictly positive binary joint distributions as well as testing-against-dependence. Our converse analysis refines the auxiliary-receiver method through three complementary steps. First, we establish an information-projection identity that identifies the posterior-divergence optimization in an existing converse with Han's exponent functional. Second, we obtain an additional excess-rate branch by retaining a mutual-information term discarded in the usual rate relaxation. Third, we develop a two-telescope upper bound whose auxiliary variables are coupled through a joint rate constraint. Combining these bounds with information-geometric matching conditions yields exact exponents for three classes of sources by matching the achievable bounds of Han and Shimokawa-Han-Amari.
ER -