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首页> 外文期刊>IEEE Transactions on Information Theory >Asymptotic Optimality in Byzantine Distributed Quickest Change Detection
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Asymptotic Optimality in Byzantine Distributed Quickest Change Detection

机译：拜占庭的渐近最优性变化检测

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The Byzantine distributed quickest change detection (BDQCD) is studied, where a fusion center monitors the occurrence of an abrupt event through a bunch of distributed sensors that may be compromised. We first consider the binary hypothesis case where there is only one post-change hypothesis and prove a novel converse to the first-order asymptotic detection delay in the large mean time to a false alarm regime. This converse is tight in that it coincides with the currently best achievability shown by Fellouris et al.; hence, the optimal asymptotic performance of binary BDQCD is characterized. An important implication of this result is that, even with compromised sensors, a 1-bit link between each sensor and the fusion center suffices to achieve asymptotic optimality. To accommodate multiple post-change hypotheses, we then formulate the multi-hypothesis BDQCD problem and again investigate the optimal first-order performance under different bandwidth constraints. A converse is first obtained by extending our converse from binary to multi-hypothesis BDQCD. Two families of stopping rules, namely the simultaneous d-th alarm and the multi-shot d-th alarm, are then proposed. Under sufficient link bandwidth, the simultaneous d-th alarm, with dbeing set to the number of honest sensors, can achieve the asymptotic performance that coincides with the derived converse bound; hence, the asymptotically optimal performance of multi-hypothesis BDQCD is again characterized. Moreover, although being shown to be asymptotically optimal only for some special cases, the multi-shot d-th alarm is much more bandwidth-efficient and energy-efficient than the simultaneous d-th alarm. Built upon the above success in characterizing the asymptotic optimality of the BDQCD, a corresponding leader-follower Stackelberg game is formulated and its solution is found.
机译：研究了拜占庭分布式最快的变化检测（BDQCD），其中融合中心通过可能受到损害的一堆分布式传感器监视突然事件的发生。我们首先考虑只有一个改变后假设的二元假设案例，并证明了一个小说逆转到一阶渐近检测延迟的大平均时间到虚假警报制度。这种匡威性紧张，因为它与Fellouris等人所示的目前最好的取得性吻合一致;因此，表征了二进制BDQCD的最佳渐近性能。这种结果的重要意义是，即使具有受损的传感器，每个传感器和融合中心之间的1位链路足以实现渐近最优值。为了适应多个后变更假设，我们将制定多假设BDQCD问题，并再次在不同的带宽约束下调查最佳的一阶性能。首先通过将逆转从二进制延伸到多假设BDQCD来获得逆转。然后提出了两个停止规则的家庭，即同时的D-TH警报和多次D-TH报警。在足够的链路带宽下，同时D-TH警报，用DBEING设置为诚实传感器的数量，可以实现与导出的逆向绑定的渐近性能;因此，再次表征了多假设BDQCD的渐近最佳性能。此外，虽然仅在某些特殊情况下被证明是渐近最佳的，但多次D-TH报警比同时D-TH报警更有带宽高效且节能。基于上述成功，在表征BDQCD的渐近最优性时，配制了相应的领导者 - 追随者Stackelberg游戏，并找到了其解决方案。

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