Fair Rate Allocation in Some Gaussian Multiaccess Channels

We can achieve all points in the capacity region of Gaussian multiple access channels by successive decoding and time-sharing. We discuss how to choose a particular point that is both Pareto optimal and fair to all users. The definition of our criterion of fairness is based on the theory of majorization. In economics, it is also known as the Lorenz order, which is used for measuring disparity in income distribution. We show that a unique solution according to such criterion exists in a large class of Gaussian multiple access channels. It turns out that the fair solution is the same as the well-known Nash bargaining solution. These two notions of fairness coincide due to the special structure of the capacity region. This provides a strong reason that we should pick it as the operational point. We also devise a fast algorithm that computes this point in some special cases