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On the Reliability Function of Distributed Hypothesis Testing Under Optimal Detection

机译：最优假设下的分布式假设检验的可靠性函数

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摘要

The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is reduced to the problem of determining the reliability function of channel codes designed for detection (in analogy to a similar result which connects the reliability function of distributed lossless compression and ordinary channel codes). Second, a single-letter random-coding bound based on a hierarchical ensemble, as well as a single-letter expurgated bound, are derived for the reliability of channel-detection codes. Both bounds are derived for a system which employs the optimal detection rule. We conjecture that the resulting random-coding bound is ensemble-tight, and consequently optimal within the class of quantization-and-binning schemes.
机译：研究了具有完整边信息的分布式假设检验问题。通过以下方法研究了两种有限速率下的误差指数之间的权衡（可靠性函数）。首先，该问题被简化为确定用于检测的信道代码的可靠性函数的问题（类似于将分布式无损压缩的可靠性函数与普通信道代码相连接的类似结果）。其次，基于信道检测码的可靠性，推导了基于分层集合的单字母随机编码边界以及单字母抽取边界。对于采用最佳检测规则的系统，得出两个边界。我们推测得到的随机编码边界是紧密集成的，因此在量化和合并方案的类别内是最优的。

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