On Compression and Coordination in Networks

Abstract: The current trends in communications suggest that the transfer of information between machines will soon predominate over the traditional human-oriented exchange. The new applications in machine-to-machine communications demand for a new type of networks that are much larger and, especially, much denser. However, there are currently many challenges that hinder an efficient deployment of such networks. In this thesis, we study some fundamental and practical aspects of two of these challenges: coordination and compression.The problem of coordination in a network is that of organizing the nodes to make them work together. The information-theoretic abstraction of this corresponds to generating actions with a desired empirical distribution. In this thesis, we construct polar codes for coordination for a variety of topologies. These codes combine elements of source coding, used to produce the actions, with elements of channel coding, used to obtain efficient descriptions. We show that our constructions achieve several fundamental coordination limits in a structured manner and with affordable complexity.Then, we consider the problem of coordinating communications to control the interference created to an external observer, measured in terms of its empirical distribution.To study the relationship between communication and interference, we introduce the notion of communication-interference capacity region. We obtain a complete characterization of this region for the single user scenario and a partial solution for a multiple user case. Our results reveal a fundamental tradeoff between communication, coordination, and interference in this type of networks.The second problem considered in this thesis, compression, involves capturing the essence of data and discarding the irrelevant aspects to obtain compact representations. This takes on a new dimension in networks, where the importance of data is no longer a local matter. In this thesis, we show that polar codes are also suitable for achieving information-theoretic bounds that involve compression in networks. More precisely, we extend our coordination constructions to realize compress-and-forward relaying with affordable complexity.In the last part of the thesis, we take a network approach to the problem of compressive sensing and develop methods for partial support set recovery. We use these methods to characterize the tradeoff between the measurement rate and the mean square error. Finally, we show that partial support recovery is instrumental in minimizing measurement outages when estimating random sparse signals.