论文标题
在无内存量化下的分布式假设检验的基本限制
A Fundamental Limit of Distributed Hypothesis Testing Under Memoryless Quantization
论文作者
论文摘要
我们研究了分布式假设测试设置，其中外围节点以无记忆的方式向融合中心发送量化的数据。 \ emph {预期} null假设下每个节点发送的位数保持限制。我们表征了错误检测的最佳衰减率（II型错误）概率，前提是很少有错误警报（I型误差），并研究通信速率和最大II类型误差率之间的权衡。我们诉诸利率延伸方法，为权衡曲线提供上限，并表明以高速率晶格量化实现了近乎最佳的性能。我们还表征了允许节点记录和量化固定数量样本的情况的折衷。此外，在汇率约束下，我们表明，通过填充水溶液获得了与权衡曲线的上限。
We study a distributed hypothesis testing setup where peripheral nodes send quantized data to the fusion center in a memoryless fashion. The \emph{expected} number of bits sent by each node under the null hypothesis is kept limited. We characterize the optimal decay rate of the mis-detection (type-II error) probability provided that false alarms (type-I error) are rare, and study the tradeoff between the communication rate and maximal type-II error decay rate. We resort to rate-distortion methods to provide upper bounds to the tradeoff curve and show that at high rates lattice quantization achieves near-optimal performance. We also characterize the tradeoff for the case where nodes are allowed to record and quantize a fixed number of samples. Moreover, under sum-rate constraints, we show that an upper bound to the tradeoff curve is obtained with a water-filling solution.
