Distributed Hypothesis Testing: Cooperation and Concurrent Detection
Distributed Hypothesis Testing: Cooperation and Concurrent Detection
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分布式假设检验：合作与并发检测
DOI：
10.1109/tit.2020.3019654
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发表时间：
2019
影响因子：
2.5
通讯作者：
A. Zaidi
中科院分区：
文献类型：
--
作者：
Pierre Escamilla;Michèle A. Wigger;A. Zaidi
考虑了一个单传感器双检测器系统，其中传感器与两个检测器通信，检测器1与检测器2通信，全部通过无噪声速率限制链路。传感器和两个检测器观察离散的无记忆源序列，其联合概率质量函数取决于一个二元假设。每个检测器的目标是以一种方式猜测二元假设，对于增加的观察长度，其中一个假设下的错误概率以最大可能的指数衰减衰减到零，而另一个假设下的错误概率可以衰减到零或任意缓慢的小正数。对于从传感器到检测器的正通信速率的设置，当两个检测器都有兴趣在相同的假设下最大化误差指数时，我们在一个特殊的情况下对独立性测试的所有可能的指数集的特征。在这种情况下，协作链路允许检测器2将其类型II误差指数增加等于在检测器1处获得的指数的量。我们还提供了一个一般的内界上的一组可实现的误差指数，在大多数情况下，在两个检测器的指数之间的权衡。当两个检测器的目标是在不同的假设下最大化的误差指数和传感器的分布是不同的两个假设下，那么我们证明了这样的权衡不存在。我们提出了一个通用的方案，允许每个检测器达到相同的指数，如果它是系统中唯一的检测器。对于两个链路上的零速率通信的设置，我们确切地描述了一组可能的指数和合作带来的增益，在两个链路上发送的比特数的函数。注意，对于这种设置，在两个检测器处实现的指数之间的折衷仅在少数特定情况下出现。在所有其他情况下，每个检测器都能实现相同的性能，就好像它是系统中唯一的检测器一样。
A single-sensor two-detectors system is considered where the sensor communicates with both detectors and Detector 1 communicates with Detector 2, all over noise-free rate-limited links. The sensor and both detectors observe discrete memoryless source sequences whose joint probability mass function depends on a binary hypothesis. The goal at each detector is to guess the binary hypothesis in a way that, for increasing observation lengths, the probability of error under one of the hypotheses decays to zero with largest possible exponential decay, whereas the probability of error under the other hypothesis can decay to zero or to a small positive number arbitrarily slow. For the setting with positive communication rates from the sensor to the detectors and when both detectors are interested in maximizing the error exponent under the same hypothesis, we characterize the set of all possible exponents in a special case of testing against independence. In this case the cooperation link allows Detector 2 to increase its Type-II error exponent by an amount that is equal to the exponent attained at Detector 1. We also provide a general inner bound on the set of achievable error exponents that shows a tradeoff between the exponents at the two detectors in most cases. When the two detectors aim at maximizing the error exponent under different hypotheses and the distribution at the Sensor is different under the two hypotheses, then we show that such a tradeoff does not exist. We propose a general scheme that allows each detector to attain the same exponent as if it was the only detector in the system. For the setting with zero-rate communication on both links, we exactly characterize the set of possible exponents and the gain brought up by cooperation, in function of the number of bits that are sent over the two links. Notice that, for this setting, tradeoffs between the exponents achieved at the two detectors arise only in few particular cases. In all other cases, each detector achieves the same performance as if it were the only detector in the system.