Achievable Degrees of Freedom on K-user MIMO Multi-way Relay Channel with Common and Private Messages

This paper investigates the achievable total degrees of freedom (DoF) of the MIMO multi-way relay channel that consists of K users, where each user is equipped with M antennas, and a decode-and-forward relay equipped with N antennas. In this channel, each user wants to convey K-1 private messages to the other users in addition to a common message to all of them. Due to the absence of direct links between the users, communication occurs through the relay in two phases; a multiple access channel phase (MAC) and a broadcast (BC) phase. We drive cut-set bounds on the total DoF of the network, and show that the network has DoF less than or equal to K min(N,M). Achievability of the upper bound is shown by using signal space alignment for network coding in the MAC phase, and zero-forcing precoding in the BC phase. We show that introducing the common messages besides the private messages leads to achieving higher total DoF than using the private messages only.