Approximate capacity of the general gaussian parallel relay network

We approximate the capacity of the Gaussian parallel relay network with general channel gains. Our strategy is to find capacity approximations for the corresponding network in the discrete superposition model and to use the fact that those are an approximation for the Gaussian capacity. The gap between our approximation and the Gaussian capacity is a constant depending only on the number of relays, hence it is a valuable characterization for the regime of high SNR and high rate.