Partial Diffusion With Quantization Over Networks

Distributed estimation over networks has drawn much attention in recent years. In the problem of distributed estimation, a set of nodes is requested to estimate some parameter of interest from noisy measurements. The nodes interact with each other to carry out the task jointly. Many algorithms have been proposed for solving the distributed estimation problem, among which the diffusion strategy is well-accepted. Information diffusion among nodes consumes bandwidth and energy resources, while in real-world applications these resources are limited. To cope with the resources constraint, partial diffusion schemes are developed. Each node only disseminates a subset of entries of interested vector in each interaction. Besides the partial transmission, quantization is another widely adopted technique for saving the communication resources. The two methods work in different aspects and can be considered jointly to make the communication more efficient. In this paper, we propose a partial diffusion scheme with quantization. An optimization problem for communication resources allocation is formulated and solved. In each interaction, the nodes will adaptively determine whether to transmit more entries or assign more bits to quantize each entry. We derive sufficient conditions for convergence of the overall algorithm. We also demonstrate the advantages of the proposed scheme in terms of both convergence speed and estimation accuracy.