An Information-Theoretic Study of Cooperation in Networks

Abstract

This thesis presents a study of cooperation in networks using the tools of information theory.

We first review the basic network models, with an emphasis on the relay channel, as this is the most basic configuration of cooperative communication. We focus on the estimate-and-forward (EAF) relaying strategy, which is a scheme that does not require the relay to decode the source messages. We investigate EAF with assignments of the auxiliary random variable that satisfy the feasibility constraint and present an alternative characterization of the classic EAF result of [Cover & El-Gamal, 1979] without a feasibility constraint, thus simplifying the description of the rate.

Next, we combine the relay channel with the broadcast channel. This combination is used to study communication over the general discrete memoryless broadcast channel (BC) with partially cooperating receivers. In our setup, the receivers are able to exchange messages over noiseless conference links of finite capacities, prior to decoding the messages sent from the transmitter. We first find the capacity region of the physically degraded BC with cooperating receivers. Then, we derive an achievable rate region for the general BC with three independent messages - two private messages and a common message, where the receivers hold a K-cycle conference. Additionally, we consider a special case of the general setup, the case of the general BC with just a single message. For this case we obtain explicit rate expressions. We also identify two scenarios in which these explicit rate expressions achieve capacity.

We then consider the discrete, memoryless, multiple-relay channel and derive an explicit achievable rate expression based on the EAF scheme. This expression is amenable to numerical evaluation. We demonstrate the benefits of this result via a discrete memoryless multiple-relay channel example, in which it is superior to multi-relay decode-and-forward. Finally, we consider the Gaussian relay channel with coded modulation at the transmitter and an orthogonal relay-destination link of finite capacity. Here we show that an EAF strategy implementing a three-level quantization outperforms the Gaussian quantization commonly used to evaluate the rates that the EAF scheme achieves in this scenario.