Degrees of freedom of the two-way interference channel with a non causal multi-antenna relay

We characterize the degrees of freedom (DoF) of the full-duplex two-way interference channel with a non causal multi-antenna relay and time-varying channels. In a two-way interference channel (IC), 4 messages and 4 transmitters/receivers form an IC in the forward direction (2 messages) and another IC in the backward direction (2 messages) which operate simultaneously in full-duplex mode. Furthermore, all nodes are permitted to interact, i.e. adapt current channel inputs to past received signals. We propose a novel block Markov coding scheme combining the ideas of interference alignment and successive decoding to achieve the full, maximal, 4 degrees of freedom asymptotically. All source/destination nodes have a single antenna while 4 antennas at the relay are sufficient to achieve the full DoF. Interestingly, this implies that the non causal relay is able to effectively mitigate interference in this two way setting - i.e. each user in the two-way interference channel is able to exchange information with its desired user at interference-free rates thanks to the relay.