新型分布式假设检验问题类的精确率指数权衡
Exact Rate Exponent Tradeoff for New Classes of Distributed Hypothesis Testing Problems
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中文总结 AI 辅助
该研究刻画新型单向分布式假设检验问题的精确率指数权衡，通过松弛上界与Han下界匹配，证明其对依赖检验及特定DSBS源为紧，适用于所有非负通信率。
中文摘要 AI 辅助
我们针对新型单向分布式假设检验问题类，刻画了其精确率指数权衡关系，通过证明借助辅助接收者技术得到的最新上界与已知下界一致实现该目标。具体而言，我们将第二类错误指数的上界松弛为与Han下界具有相同内部函数形式的形式，仅在外部率约束上存在差异。此外，我们证明该上界对依赖检验及双对称二元源（DSBS）是紧的，其中原假设下的交叉概率为κ₀，备择假设下为κ₁，且满足0 < κ₁ ≤ κ₀ < 1/2。DSBS源的精确错误指数刻画适用于所有通信率R ≥ 0。
英文摘要
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 $0 < κ_1 < κ_0 < \frac12$. The characterization of the exact error exponent for the DSBS source holds for every communication rate $R \geq 0$.
