An achievable rate region for the two-way multiple relay channel

An achievable rate-region for the two-way multiple-relay channel is proposed using decode-forward block Markovian coding. We identify a fundamental tension between the information flow in both directions that leads to an intractable number of decode-forward schemes and achievable rate regions, none of which are universally better than the others. We introduce a new concept in decode-forward coding called ranking, and discover that each of these rate regions are different realizations of a single expression that depends on the rank assignment. This discovery makes it possible to characterize the complete achievable rate region that includes all of the interesting decode-forward schemes and corresponding rate regions.