We study a binary distributed hypothesis testing problem where two agents observe correlated binary vectors and communicate compressed information at the same rate to a central decision maker. In particular, we study linear compression schemes and show that simple truncation is the best linear scheme in two cases: (1) testing opposite signs of the same magnitude of correlation, and (2) testing for or against independence. We conjecture, supported by numerical evidence, that truncation is the best linear code for testing any correlations of opposite signs. Further, for testing against independence, we also compute classical random coding exponents and show that truncation, and consequently any linear code, is strictly suboptimal.

翻译：我们研究了一个二元分布式假设检验问题，其中两个智能体观测相关的二元向量，并以相同速率向中央决策者传输压缩信息。具体而言，我们研究了线性压缩方案，并证明在以下两种情况下，简单的截断操作是最优的线性方案：(1) 检验具有相同幅度但符号相反的相关系数；(2) 检验相关性或独立性的存在。基于数值证据的支持，我们推测截断操作是检验任意符号相反相关性的最优线性码。此外，在检验独立性的场景中，我们还计算了经典随机编码的指数函数，并证明截断操作（进而任何线性码）均具有严格的次优性。