标题： 具有劣质传感器的二进制中继树的误概率界 显示英文标题

标题： Error Probability Bounds for Binary Relay Trees with Crummy Sensors

摘要： 我们研究了与平衡二元中继树相关的检测错误概率问题，其中传感器节点以一定概率发生故障。 我们考虑了 N 个相同的独立的劣质传感器，这些传感器由树的叶节点表示。 树的根节点表示融合中心，负责在两种假设之间做出最终决策。 每个其他节点都是一个中继节点，它最多将两个二进制消息融合成一个二进制消息，并将新消息转发给其父节点。 我们推导出融合中心处总错误概率的紧上界和下界，并将其表示为 N 的函数，同时分析了总错误概率随 N 收敛到 0 的速度。我们证明了总错误概率的收敛是非线性的，且具有与无传感器故障的平衡二元中继树相同的衰减指数。 我们还表明，即使单个传感器的总错误概率收敛到 1/2，失效概率收敛到 1，只要收敛速率足够慢，总错误概率仍然会收敛到 0。 显示英文摘要

摘要： We study the detection error probability associated with balanced binary relay trees, in which sensor nodes fail with some probability. We consider N identical and independent crummy sensors, represented by leaf nodes of the tree. The root of the tree represents the fusion center, which makes the final decision between two hypotheses. Every other node is a relay node, which fuses at most two binary messages into one binary message and forwards the new message to its parent node. We derive tight upper and lower bounds for the total error probability at the fusion center as functions of N and characterize how fast the total error probability converges to 0 with respect to N. We show that the convergence of the total error probability is sub-linear, with the same decay exponent as that in a balanced binary relay tree without sensor failures. We also show that the total error probability converges to 0, even if the individual sensors have total error probabilities that converge to 1/2 and the failure probabilities that converge to 1, provided that the convergence rates are sufficiently slow.