A Simplified Dependence Balance-Based Outer Bound for Gaussian MAC With Noisy Feedback

In 2011, Tandon and Ulukus gave an outer bound on the capacity region of the two-user Gaussian multiple access channel (MAC) with noisy feedback based on the idea of dependence balance (DB). This outer bound is described using a covariance matrix with three independent parameters. In this letter, we simplify their results and express the DB-based outer bound in a form using only one parameter. From the new form, it is easy to see that when the noise powers at the transmitters go to either zero or infinity, the DB bound is tight and yields the capacity region of the Gaussian MAC with perfect and no feedback, respectively. Using the simplified form of the DB bound, we also derive a new upper bound on the maximum weighted sum rate for the Gaussian MAC with noisy feedback which is tight for the two cases just described.