On the DoF of two-way 2 × 2 × 2 relay networks with or without relay caching

Two-way relay is potentially an effective approach to spectrum sharing and aggregation by allowing simultaneous bidirectional transmissions between source-destinations pairs. This paper studies the two-way 2×2×2 relay network, a class of four-unicast networks, where there are four source/destination nodes and two relay nodes, with each source sending a message to its destination. We show that without relay caching the total degrees of freedom (DoF) is bounded from above by 8/3, indicating that bidirectional links do not double the DoF (It is known that the total DoF of one–way 2× 2× 2 relay network is 2.). Further, we show that the DoF of 8/3 is achievable for the two-way 2× 2× 2 relay network with relay caching. Finally, even though the DoF of this network is no more than 8/3 for generic channel gains, DoF of 4 can be achieved for a symmetric configuration of channel gains.