1-bit Compressive Diffusion in Networks Based on Bayesian Inference

Compressive diffusion strategy, especially the 1-bit compressive diffusion, has the potential to greatly reduce the communication load between nodes in a network for distributed parameter estimation. However, how to deal with the hybrid data, i.e., the 1-bit quantized external information from other nodes and the high-precision local data, has heavy impact on the overall estimation performance. Most existing estimation algorithms based on Least Mean Square (LMS) cannot work very well in such a context, i.e., the combination of the above information is not guaranteed beneficial in general unless certain combination rule is properly chosen. In this paper, from a perspective of Bayesian inference framework instead, a parameter estimation algorithm is proposed for 1-bit compressive diffusion. Based on the vertex-message inference, the inherent combination policy assigns different weights to measurements depending on their data types and degrees of uncertainty. In this way, nodes in the network can always take advantage of the extra information in 1-bit exchanged data to enhance the accuracy of local estimation, and at the same time avoid any possible performance loss caused by the high uncertainty of compressive data.