A distributed binary hypothesis testing (HT) problem over a noisy (discrete and memoryless) channel studied previously by the authors is investigated from the perspective of the strong converse property. It was shown by Ahlswede and Csisz\'{a}r that a strong converse holds in the above setting when the channel is rate-limited and noiseless. Motivated by this observation, we show that the strong converse continues to hold in the noisy channel setting for a special case of HT known as testing against independence (TAI). The proof utilizes the blowing up lemma and the recent change of measure technique of Tyagi and Watanabe as the key tools.

中文翻译：

---

用于在嘈杂信道上测试独立性的强对话

从强逆性质的角度研究了作者先前研究的噪声（离散和无记忆）信道上的分布式二元假设检验（HT）问题。Ahlswede 和 Csisz\'{a}r 表明，当信道限速且无噪声时，上述设置中存在强逆。受此观察的启发，我们表明，对于称为独立性测试 (TAI) 的 HT 特殊情况，强逆向继续在嘈杂的通道设置中成立。证明以 Tyagi 和 Watanabe 的爆炸引理和最近的测量技术变化为关键工具。