Consensus is a common method for computing a function of the data distributed among the nodes of a network. Of particular interest is distributed average consensus, whereby the nodes iteratively compute the sample average of the data stored at all the nodes of the network using only near-neighbor communications. In real-world scenarios, these communications must undergo quantization, which introduces distortion to the internode messages. In this thesis, a model for the evolution of the network state statistics at each iteration is developed under the assumptions of Gaussian data and additive quantization error. It is shown that minimization of the communication load in terms of aggregate source coding rate can be posed as a generalized geometric program, for which an equivalent convex optimization can efficiently solve for the global minimum. Optimization procedures are developed for rate-distortion-optimal vector quantization, uniform entropy-coded scalar quantization, and fixed-rate uniform quantization. Numerical results demonstrate the performance of these approaches. For small numbers of iterations, the fixed-rate optimizations are verified using exhaustive search. Comparison to the prior art suggests competitive performance under certain circumstances but strongly motivates the incorporation of more sophisticated coding strategies, such as differential, predictive, or Wyner-Ziv coding.
翻译:共识是计算网络节点之间分布的数据函数的通用方法。 特别令人感兴趣的是分配平均共识, 节点迭代计算网络所有节点仅使用近邻通信存储的数据的样本平均数。 在现实世界情景中, 这些通信必须经过量化, 这会扭曲内向电文。 在此论文中, 在高斯数据假设和添加量量化错误的假设下, 开发了网络状态每次迭代的统计演进模式。 显示以综合源编码率计算的通信负荷最小化可以作为一种通用的几何计法程序, 而对于这个程序, 等量的 convex优化可以有效地解决全球最低量问题。 优化程序必须经过量化, 以电压- 调控- 优化矢量定量化、 统一调制电磁度定量化和固定率统一四分化。 数值结果显示了这些方法的性能。 对于少量的迭代点, 固定值优化的节率优化是使用精确的精确的搜索方法, 或者以更强的预估方式进行预估。