User-relay duality in cyclic interference alignment for cascaded two-way relay networks

We investigate a cascaded two-way relay network with K users and K relays alternately arranged in terms of a conceptual channel model based on polynomial rings. This channel model is inspired by cyclic codes and can be applied to time interference alignment by propagation delay for instance. A multiple-unicast problem for both the open-loop case, i. e., a straight line network of alternately arranged users and relays, and the corresponding closed-loop topology is considered. We provide an upper bound on the degrees of freedom which is achieved by means of signal alignment and interference alignment. Moreover, we observe a dual relationship for the closed-loop network if the roles of users and relays are swapped.