Source Coding in Networks with Covariance Distortion Constraints

We consider a source coding problem with a network scenario in mind, and formulate it as a remote vector Gaussian Wyner-Ziv problem under covariance matrix distortions. We define a notion of minimum for two positive-definite matrices based on which we derive an explicit formula for the rate-distortion function (RDF). We then study the special cases and applications of this result. We show that two well-studied source coding problems, i.e. remote vector Gaussian Wyner-Ziv problems with mean-squared error and mutual information constraints are in fact special cases of our results. Finally, we apply our results to a joint source coding and denoising problem. We consider a network with a centralized topology and a given weighted sum-rate constraint, where the received signals at the center are to be fused to maximize the output SNR while enforcing no linear distortion. We show that one can design the distortion matrices at the nodes in order to maximize the output SNR at the fusion center. We thereby bridge between denoising and source coding within this setup

Optimized Data Rate Allocation for Dynamic Sensor Fusion over Resource Constrained Communication Networks

This paper presents a new method to solve a dynamic sensor fusion problem. We consider a large number of remote sensors which measure a common Gauss-Markov process and encoders that transmit the measurements to a data fusion center through the resource restricted communication network. The proposed approach heuristically minimizes a weighted sum of communication costs subject to a constraint on the state estimation error at the fusion center. The communication costs are quantified as the expected bitrates from the sensors to the fusion center. We show that the problem as formulated is a difference-of-convex program and apply the convex-concave procedure (CCP) to obtain a heuristic solution. We consider a 1D heat transfer model and 2D target tracking by a drone swarm model for numerical studies. Through these simulations, we observe that our proposed approach has a tendency to assign zero data rate to unnecessary sensors indicating that our approach is sparsity promoting, and an effective sensor selection heuristic