Exploiting Structure in Cooperative Networks

In this thesis we explore two examples of how to exploit structure in networks with cooperative nodes. 1) In the first direction, we explore the impact of message structure and how it may (or may not) be exploited to increase capacity depending on how this ``matches'' the channel's structure. As an example of this concept, the Inverse Compute-and-Forward (ICF) problem is proposed and studied, where we show that $K$-wise message correlations when $K>2$, cannot be utilized to improve rate regions in a Gaussian MAC channel. 2) In the second direction we work towards explicitly exploiting channel structure in a zero-error primitive relay channel scenario. The problem of communicating over a primitive relay channel without error is for the first time proposed, with the goal of exploring and fulfilling the intuition that the central role of a relay is to only deliver ''what the destination needs''. A novel relaying scheme termed ``Colour-and-Foward'' is proposed and is shown to be the most efficient way of compressing signals at the relay terminal, for any fixed number of channel uses, when enabling an effectively full cooperation between the relay and the destination terminals, i.e. achieving the single-input multi-output (SIMO) upper bound, is required. This Colour-and-Forward relaying is designed by an explicit exploit of the channel structure and directly embodies the intuition of having relay transmit ``only what the destination needs''.