In this paper we revisit the binary hypothesis testing problem with one-sided compression. Specifically we assume that the distribution in the null hypothesis is a mixture distribution of iid components. The distribution under the alternative hypothesis is a mixture of products of either iid distributions or finite order Markov distributions with stationary transition kernels. The problem is studied under the Neyman-Pearson framework in which our main interest is the maximum error exponent of the second type of error. We derive the optimal achievable error exponent and under a further sufficient condition establish the maximum $\epsilon$-achievable error exponent. It is shown that to obtain the latter, the study of the exponentially strong converse is needed. Using a simple code transfer argument we also establish new results for the Wyner-Ahlswede-K{\"o}rner problem in which the source distribution is a mixture of iid components.

翻译：在本文中,我们用片面压缩来重新审视二进制假设测试问题。 具体地说, 我们假设无效假设中的分布是iid 组件的混合分布。 替代假设下的分布是iid 分布或有定序的Markov 分布与固定的过渡内核的混合产品。 这个问题在Neyman- Pearson 框架下研究, 我们的主要兴趣就是二类错误的最大误差引出。 我们得出最佳的可实现误差, 并在另一个足够条件下确定最高值$\ epsilon$ 可实现的误差。 显示要获得后一种误差, 就需要对指数强烈的反差进行研究 。 使用简单的代码转换参数, 我们还为Wyner- Ahlswede- K o}rner 问题设定了新的结果, 其中源分配是iid 组件的混合物 。