Capacity of Gaussian noise channels with side information and feedback

Abstract

In wireless communication systems, the communication channel is often modeled as a fading multiaccess channel with time-varying multipath. Because of the mobility of the users and the varying number of users, the transmission conditions are constantly changing. These characteristics of the channel, as well as the ever-growing number of users competing for limited resources, call for an efficient use of the available power and bandwidth resources. In order to achieve a maximum system efficiency, the transmission conditions have to be constantly monitored and used to update the transmission strategies. The transmitters usually have some form of information regarding the channel behavior. The main question of interest is to determine how to best use this information in order to increase the transmission rates, decrease the error probability and conserve resources. In this thesis, we present an information-theoretic analysis of the single-user channel with side information and feedback. The first part of this work is devoted to the discrete-time, finite-state additive white Gaussian noise channel. Under perfect instantaneous side-information, the capacity achieving power allocation is determined by the well-known water-filling procedure. The basic water-filling power allocation is extended to include minimal rate and / or maximal power constraints. Various imperfections in the side-information and their influence on capacity and the power allocation are studied next. These imperfections include delayed side-information, errors in the transmission of side-information, and errors in the estimation of the channel conditions. We also present a universal power control algorithm that does not assume knowledge of the statistical behavior of the channel. The feedback capacity of the finite-state channel is investigated and upper and lower bounds are derived. In the second part of the thesis, we concentrate on the feedback capacity of the colored Gaussian noise channel. The capacity of this channel is still an open problem and most research work has focused on finding upper bounds. We propose a new, tighter lower bound on the feedback capacity. This bound is very general in the sense that it can be applied to any noise covariance matrix and can be computed for both the finite and the infinite time horizon cases. A sufficient condition is obtained on the average available power such that feedback strictly increases capacity. An interesting and intriguing consequence is reached that sheds new light on the role of the feedback. Specifically it is shown that feedback should not be used to cancel out the noise process, but rather to transmit information about the noise to the receiver. Finally, two problems related to the Gaussian multi-access channel are examined. First, new bounds on the maximum sum rate and the capacity region with feedback are derived. Several previously published bounds can be viewed as special cases of these bounds. Second, we compute the optimal power allocation vector that guarantees that a fixed target rate tuple is achievable, while at the same time minimizing the sum of the transmit powers used by the individual users. The optimal decoding order is shown to be independent of the target rate tuple.