Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Non-stationary/Unstable Linear Systems

Stabilization of non-stationary linear systems over noisy communication channels is considered. Stochastically stable sources, and unstable but noise-free or bounded-noise systems have been extensively studied in information theory and control theory literature since 1970s, with a renewed interest in the past decade. There have also been studies on non-causal and causal coding of unstable/non-stationary linear Gaussian sources. In this paper, tight necessary and sufficient conditions for stochastic stabilizability of unstable (non-stationary) possibly multi-dimensional linear systems driven by Gaussian noise over discrete channels (possibly with memory and feedback) are presented. Stochastic stability notions include recurrence, asymptotic mean stationarity and sample path ergodicity, and the existence of finite second moments. Our constructive proof uses random-time state-dependent stochastic drift criteria for stabilization of Markov chains. For asymptotic mean stationarity (and thus sample path ergodicity), it is sufficient that the capacity of a channel is (strictly) greater than the sum of the logarithms of the unstable pole magnitudes for memoryless channels and a class of channels with memory. This condition is also necessary under a mild technical condition. Sufficient conditions for the existence of finite average second moments for such systems driven by unbounded noise are provided.Comment: To appear in IEEE Transactions on Information Theor

Strong Coordination over Multi-hop Line Networks

We analyze the problem of strong coordination over a multi-hop line network in which the node initiating the coordination is a terminal network node. We assume that each node has access to a certain amount of randomness that is local to the node, and that the nodes share some common randomness, which are used together with explicit hop-by-hop communication to achieve strong coordination. We derive the trade-offs among the required rates of communication on the network links, the rates of local randomness available to network nodes, and the rate of common randomness to realize strong coordination. We present an achievable coding scheme built using multiple layers of channel resolvability codes, and establish several settings in which this scheme is proven to offer the best possible trade-offs.Comment: 35 pages, 9 Figures, 4 Tables. A part of this work were published in the 2015 IEEE Information Theory Workshop, and a part was accepted for publication in the 50th Annual Conference on Information Sciences and System

Mini-Workshop: Entropy, Information and Control

This mini-workshop was motivated by the emerging field of networked control, which combines concepts from the disciplines of control theory, information theory and dynamical systems. Many current approaches to networked control simplify one or more of these three aspects, for instance by assuming no dynamical disturbances, or noiseless communication channels, or linear dynamics. The aim of this meeting was to approach a common understanding of the relevant results and techniques from each discipline in order to study the major, multi-disciplinary problems in networked control

DISTRIBUTED ESTIMATION OVER NETWORKS WITH COMMUNICATION COSTS

We analyze how distributed or decentralized estimation can be performed over networks, when there is a price to be paid whenever nodes in the network communicate with each other. The work here has application especially in the network control systems. Assume that different nodes in the network can track perfectly or with imperfectly some stochastic processes, while other nodes in the network need to estimate these stochastic processes. The nodes which can observe the stochastic processes can send information directly to the nodes which need to estimate the processes, or information can be sent to intermediate nodes. When each transmission is performed a cost for communication is paid. The goal of the network is to optimize jointly a cost which consists both of a function of the estimation error and a function of the transmission cost. We show here that for some simple topologies the decision to send information over the network is a threshold policy, while the estimators are linear estimators which resemble with the Kalman-filter. For the result dealing with simple topologies we have proved the results using majorization theory. It is also shown here both analytically and numerically that things can immediately become quite complicated. If we take into consideration multidimensional problems or problems with multiple agents and/or transmission noise, the optimal strategies can no longer be found analytically and it can be quite difficult to compute numerically the optimal strategies