Single Bit and Reduced Dimension Diffusion Strategies Over Distributed Networks

We introduce novel diffusion based adaptive estimation strategies for distributed networks that have significantly less communication load and achieve comparable performance to the full information exchange configurations. After local estimates of the desired data is produced in each node, a single bit of information (or a reduced dimensional data vector) is generated using certain random projections of the local estimates. This newly generated data is diffused and then used in neighboring nodes to recover the original full information. We provide the complete state-space description and the mean stability analysis of our algorithms.Comment: Submitted to the IEEE Signal Processing Letter

Compressive Diffusion Strategies Over Distributed Networks for Reduced Communication Load

We study the compressive diffusion strategies over distributed networks based on the diffusion implementation and adaptive extraction of the information from the compressed diffusion data. We demonstrate that one can achieve a comparable performance with the full information exchange configurations, even if the diffused information is compressed into a scalar or a single bit. To this end, we provide a complete performance analysis for the compressive diffusion strategies. We analyze the transient, steady-state and tracking performance of the configurations in which the diffused data is compressed into a scalar or a single-bit. We propose a new adaptive combination method improving the convergence performance of the compressive diffusion strategies further. In the new method, we introduce one more freedom-of-dimension in the combination matrix and adapt it by using the conventional mixture approach in order to enhance the convergence performance for any possible combination rule used for the full diffusion configuration. We demonstrate that our theoretical analysis closely follow the ensemble averaged results in our simulations. We provide numerical examples showing the improved convergence performance with the new adaptive combination method.Comment: Submitted to IEEE Transactions on Signal Processin

Team-optimal distributed MMSE estimation in general and tree networks

We construct team-optimal estimation algorithms over distributed networks for state estimation in the finite-horizon mean-square error (MSE) sense. Here, we have a distributed collection of agents with processing and cooperation capabilities. These agents observe noisy samples of a desired state through a linear model and seek to learn this state by interacting with each other. Although this problem has attracted significant attention and been studied extensively in fields including machine learning and signal processing, all the well-known strategies do not achieve team-optimal learning performance in the finite-horizon MSE sense. To this end, we formulate the finite-horizon distributed minimum MSE (MMSE) when there is no restriction on the size of the disclosed information, i.e., oracle performance, over an arbitrary network topology. Subsequently, we show that exchange of local estimates is sufficient to achieve the oracle performance only over certain network topologies. By inspecting these network structures, we propose recursive algorithms achieving the oracle performance through the disclosure of local estimates. For practical implementations we also provide approaches to reduce the complexity of the algorithms through the time-windowing of the observations. Finally, in the numerical examples, we demonstrate the superior performance of the introduced algorithms in the finite-horizon MSE sense due to optimal estimation. © 2017 Elsevier Inc