On the Capacity Gap of Gaussian Multi-Way Relay Channels

Multi-way relaying is a promising approach to enhance the spectral efficiency in multi-user communication systems. Several relaying strategies have been proposed recently to be used in multi-user communication systems. In this paper, we analyze the gap between the achievable rate of some of these relaying techniques and the capacity of the Gaussian multiway relay channels (GMWRCs). To this end, for a symmetric GMWRC with K users, we prove that lattice-based relaying guarantees a gap less than 1/2(K-1) bit from the capacity upper bound. Also, we show that decode-and-forward and amplify-and-forward relaying may have a larger capacity gap than 1/2(K-1) bit depending on the relay and users' SNR. Then, we find the SNR regions where these two techniques also ensure a 1/2(K-1)-bit gap.