Optimal Transmit Covariance for Ergodic MIMO Channels

In this paper we consider the computation of channel capacity for ergodic multiple-input multiple-output channels with additive white Gaussian noise. Two scenarios are considered. Firstly, a time-varying channel is considered in which both the transmitter and the receiver have knowledge of the channel realization. The optimal transmission strategy is water-filling over space and time. It is shown that this may be achieved in a causal, indeed instantaneous fashion. In the second scenario, only the receiver has perfect knowledge of the channel realization, while the transmitter has knowledge of the channel gain probability law. In this case we determine an optimality condition on the input covariance for ergodic Gaussian vector channels with arbitrary channel distribution under the condition that the channel gains are independent of the transmit signal. Using this optimality condition, we find an iterative algorithm for numerical computation of optimal input covariance matrices. Applications to correlated Rayleigh and Ricean channels are given.Comment: 22 pages, 14 figures, Submitted to IEEE Transactions on Information Theor

A Minimal Set of Shannon-type Inequalities for Functional Dependence Structures

The minimal set of Shannon-type inequalities (referred to as elemental inequalities), plays a central role in determining whether a given inequality is Shannon-type. Often, there arises a situation where one needs to check whether a given inequality is a constrained Shannon-type inequality. Another important application of elemental inequalities is to formulate and compute the Shannon outer bound for multi-source multi-sink network coding capacity. Under this formulation, it is the region of feasible source rates subject to the elemental inequalities and network coding constraints that is of interest. Hence it is of fundamental interest to identify the redundancies induced amongst elemental inequalities when given a set of functional dependence constraints. In this paper, we characterize a minimal set of Shannon-type inequalities when functional dependence constraints are present.Comment: 5 pagers, accepted ISIT201