A class of Bi-directional multi-relay protocols

In a bi-directional relay channel, two nodes wish to exchange independent messages over a shared wireless half-duplex channel with the help of relays. Recent work has considered information theoretic limits of the hi-directional relay channel with a single relay. In this work we consider bidirectional relaying with multiple relays. We derive achievable rate regions and outer bounds for half-duplex protocols with multiple decode and forward relays and compare these to the same protocols with amplify and forward relays in an additive white Gaussian noise channel. We consider three novel classes of half-duplex protocols: the (m, 2) 2 phase protocol with m relays, the (m, 3) 3 phase protocol with m relays, and general (m, t) Multiple Hops and Multiple Relays (MHMR) protocols, where in is the total number of relays and 3 < t <= in + 2 is the number of temporal phases in the protocol. Finally, we provide a comprehensive treatment of the MHMR protocols with decode and forward relaying and amplify and forward relaying in Gaussian noise, obtaining their respective achievable rate regions, outer bounds and relative performance at different SNRs. The (m,m + 2) DF MHMR protocol achieves the largest rate region under simulated channel conditions.