The DoF of Two-Way Butterfly Networks

This letter studies the two-way butterfly network, a class of two-way four-unicast networks. We first show that bidirectional links do not increase the degrees of freedom for this network, thus giving the first example of a network to the best of our knowledge, where bidirectional links do not increase the degrees of freedom. Furthermore, we show that sufficient caching at the relays or increasing the number of antennas at the relays can double the degrees of freedom for the two-way butterfly network.