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. In this study, 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, is studied. They 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, they 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.