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Distributed Sequential Hypothesis Testing With Quantized Message-Exchange

机译：具有量化消息交换的分布式顺序假设检验

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摘要

This work considers the cooperative sequential hypothesis testing problem in a distributed network with quantized communication channels. The sensors observe independent sequences of samples and in the meantime, exchange their local information in the form of quantized statistics at every sampling interval. The communication links are represented as an undirected graph. In this distributed setup, every sensor performs its own sequential test based on the local samples and the messages from the neighbour sensors. Our goal is to devise the distributed sequential test that comprises the quantization scheme, the message-exchange protocol and the test procedure such that every sensor in the network fully exploits the network diversity and achieves the (asymptotically) optimal performance in terms of the stopping time. In particular, two distributed sequential tests are proposed based on different quantization schemes and a quantized message-exchange protocol that satisfies certain conditions. The first quantization scheme uniformly quantizes the local statistic at each sensor and at every sampling interval; the second one hinges on a modified level-triggered quantization technique, and resembles the Lebesgue sampling of the running local statistic. Our analyses show that the uniform quantization based distributed sequential test yields sub-optimal performance, while the one based on level-triggered quantization achieves the order-2 asymptotically optimal performance at every sensor for any fixed quantization step-size. Furthermore, we generalize the proposed sequential tests to the cluster-based network. Numerical results are provided to corroborate our analyses and demonstrate the effectiveness of the proposed sequential tests.
机译：这项工作考虑了在具有量化通信信道的分布式网络中的协作顺序假设检验问题。传感器观察独立的样本序列，与此同时，在每个采样间隔以量化统计的形式交换其本地信息。通信链接表示为无向图。在这种分布式设置中，每个传感器都基于本地样本和来自相邻传感器的消息执行自己的顺序测试。我们的目标是设计包括量化方案，消息交换协议和测试过程的分布式顺序测试，以使网络中的每个传感器都充分利用网络多样性，并在停止时间方面达到（渐近）最佳性能。特别是，基于不同的量化方案和满足某些条件的量化消息交换协议，提出了两个分布式顺序测试。第一种量化方案对每个传感器和每个采样间隔的本地统计量进行统一量化。第二种方法依赖于改进的电平触发量化技术，类似于运行中的本地统计数据的Lebesgue采样。我们的分析表明，基于均匀量化的分布式顺序测试会产生次优的性能，而基于电平触发的量化则可以在每个传感器上以任何固定的量化步长实现2阶渐近最优性能。此外，我们将建议的顺序测试推广到基于集群的网络。提供的数值结果证实了我们的分析结果，并证明了所提出的顺序测试的有效性。

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