In this paper, we investigate distributed inference schemes, over binary-valued Markov random fields, which are realized by the belief propagation (BP) algorithm. We first show that a decision variable obtained by the BP algorithm in a network of distributed agents can be approximated by a linear fusion of all the local log-likelihood ratios. The proposed approach clarifies how the BP algorithm works, simplifies the statistical analysis of its behavior, and enables us to develop a performance optimization framework for the BP-based distributed inference systems. Next, we propose a blind learning-adaptation scheme to optimize the system performance when there is no information available a priori describing the statistical behavior of the wireless environment concerned. In addition, we propose a blind threshold adaptation method to guarantee a certain performance level in a BP-based distributed detection system. To clarify the points discussed, we design a novel linear-BP-based distributed spectrum sensing scheme for cognitive radio networks and illustrate the performance improvement obtained, over an existing BP-based detection method, via computer simulations.

中文翻译：

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分布式检测的线性化置信度传播优化

在本文中，我们研究了通过置信传播 (BP) 算法实现的二值马尔可夫随机场上的分布式推理方案。我们首先表明，通过 BP 算法在分布式代理网络中获得的决策变量可以通过所有局部对数似然比的线性融合来近似。所提出的方法阐明了 BP 算法的工作原理，简化了对其行为的统计分析，并使我们能够为基于 BP 的分布式推理系统开发性能优化框架。接下来，我们提出了一种盲学习适应方案，以在没有可用的先验信息来描述相关无线环境的统计行为时优化系统性能。此外，我们提出了一种盲阈值自适应方法，以在基于 BP 的分布式检测系统中保证一定的性能水平。为了阐明所讨论的要点，我们为认知无线电网络设计了一种新颖的基于线性 BP 的分布式频谱感知方案，并通过计算机模拟说明了相对于现有的基于 BP 的检测方法所获得的性能改进。