The role of feedback in multiuser information theory

Feedback does not increase the capacity of single user memoryless channels. But for memoryless multi-user channels with many senders and receivers, feedback helps the senders and receivers to cooperate more effectively and enables an increase in the total rate of communication. In this thesis, we will explore the various roles of feedback in communication networks.; For a multiple access channel (many senders sending information to a single receiver), we show how feedback helps the senders cooperate and show that for an m-user multiple access channel, feedback increases the total capacity by at most a factor of m. For the Gaussian multiple access channel, feedback at most doubles the total capacity.; For simple multiple access channels, feedback does not increase capacity. We will prove a source channel separation theorem for such channels and show how we can analyze cascades of such channels with deterministic broadcast channels.; For a broadcast channel (a single sender sending information to many receivers), we illustrate how feedback helps to increase the capacity by enabling the sender to send common information to the receivers. We also show how feedback increases the capacity of a Gaussian interference channel (two senders and two receivers with crosstalk) and derive inner and outer bounds on its capacity region.; We describe the role of feedback in a general network of senders and receivers and describe an outer bound on the rate of flow of information in such a network. We study some of the properties of these bounds, which are stated in terms of the mutual information between subsets of random variables. We derive some inequalities for entropy rates of subsets and show how they can be used to derive new inequalities for determinants of positive matrices.; The flow of information bounds for a general network allow us to unify the earlier results on the role of feedback in multi-user communication channels. For simple multi-user networks, feedback does not help very much, but in general, feedback could open up new communication paths that are more efficient than the paths available without feedback and could increase capacity by an arbitrarily large factor.