Asymptotically Optimal Stochastic Encryption for Quantized Sequential Detection in the Presence of Eavesdroppers
Asymptotically Optimal Stochastic Encryption for Quantized Sequential Detection in the Presence of Eavesdroppers
复制标题
存在窃听者时用于量化顺序检测的渐近最优随机加密
DOI：
10.1109/tit.2019.2955473
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发表时间：
2017
影响因子：
2.5
通讯作者：
Xiaodong Wang
中科院分区：
文献类型：
--
作者：
Jiangfan Zhang;Xiaodong Wang
我们考虑在窃听者存在的情况下，基于量化数据的序列检测。采用随机加密作为对策，将每个传感器的量化位按照一定的概率进行翻转，翻转概率只有合法融合中心（LFC）知道，而窃听融合中心（EFC）不知道。因此，LFC采用最优序列概率比检验（SPRT）进行序列检测，而EFC采用不匹配的SPRT （MSPRT）进行序列检测。我们用期望样本量作为消失误差概率的函数来描述MSPRT的渐近性能。我们表明，当LFC和EFC的检测错误概率设置为相同时，每个对称随机加密都是无效的，因为它导致LFC和EFC的期望样本量相同。接下来，在小检测误差概率的渐近范围内，我们表明每个随机加密都会通过增加期望样本量来降低LFC处量化顺序检测的性能，并且EFC所需的期望样本量不少于LFC所需的期望样本量。在此基础上，研究了最优随机加密，即最大限度地提高EFC和LFC期望样本大小之间的差值。虽然该优化问题是非凸的，但我们证明了如果随机加密引起的LFC期望样本量增加的可接受容限足够小，则可以解析得到全局最优随机加密；而且，最优方案只翻转一种类型的量化位（即1或0），而保持另一种类型不变。
We consider sequential detection based on quantized data in the presence of eavesdropper. Stochastic encryption is employed as a counter measure that flips the quantization bits at each sensor according to certain probabilities, and the flipping probabilities are only known to the legitimate fusion center (LFC) but not the eavesdropping fusion center (EFC). As a result, the LFC employs the optimal sequential probability ratio test (SPRT) for sequential detection whereas the EFC employs a mismatched SPRT (MSPRT). We characterize the asymptotic performance of the MSPRT in terms of the expected sample size as a function of the vanishing error probabilities. We show that when the detection error probabilities are set to be the same at the LFC and EFC, every symmetric stochastic encryption is ineffective in the sense that it leads to the same expected sample size at the LFC and EFC. Next, in the asymptotic regime of small detection error probabilities, we show that every stochastic encryption degrades the performance of the quantized sequential detection at the LFC by increasing the expected sample size, and the expected sample size required at the EFC is no fewer than that is required at the LFC. Then the optimal stochastic encryption is investigated in the sense of maximizing the difference between the expected sample sizes required at the EFC and LFC. Although this optimization problem is nonconvex, we show that if the acceptable tolerance of the increase in the expected sample size at the LFC induced by the stochastic encryption is small enough, then the globally optimal stochastic encryption can be analytically obtained; and moreover, the optimal scheme only flips one type of quantized bits (i.e., 1 or 0) and keeps the other type unchanged.
影响因子：
2.5
作者：
Li, Shang;Li, Xiaoou;Liu, Jingchen
通讯作者：
Liu, Jingchen