| Summary: | We propose an information theoretic framework for scheduling the transmissions in a two-way multi-hop network. First we investigate some long standing open problems that were encountered during the course of the research. To illustrate their difficulty, we describe some failed attempts at resolving them. We then introduce the two-way one-relay channel. It turns out that the achievable rate region of this network has a nice interpretation, especially when viewed in the context of the open problems examined earlier. Motivated by this observation, we attempt to extend this achievable region to the two-way two-relay channel. In the process, we expose a fundamental deadlock problem in which each relay needs to decode before the other in order to enable mutual assistance. Our most important contribution is a resolution to this deadlock problem; we add an additional constraint that ensures some relay can decode at least one message before the other relay. Furthermore, we also introduce several coding schemes to prove that the additional constraint is indeed sufficient. Our schemes also show that information theory provides unique insight into scheduling the transmissions of multi-hop networks.
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