On compute-and-forward with feedback

We consider a Gaussian multiple-access channel where each user's message is identified with a vector of elements from a finite field, and the receiver's goal is to decode a linear combination of these finite field vectors. It is further assumed that each transmitter can causally observe the channel's output through a clean feedback link. We propose a novel coding scheme for this setup, which can be seen as an extension of the Cover-Leung scheme for the computation problem. This scheme is shown to achieve computation rates higher than the best known computation rates for the same scenario without feedback. In particular, for the symmetric two-user Gaussian multiple-access channel, the proposed scheme attains a symmetric computation rate greater than 1/2 log(3/4 + SNR).