Bi-directional half-duplex protocols with multiple relays

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 bi-directional relay channel with a single relay. In this work we consider bi-directional 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 halfduplex 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 m is the total number of relays and 3 < t ≤ m+2 is the number of temporal phases in the protocol. The (m, 2) and (m, 3) protocols extend previous bi-directional relaying protocols for a single m = 1 relay, while the (m, t) protocol efficiently combines multi-hop routing with network coding. Finally, we provide a comprehensive treatment of the MHMR protocols with decode and forward relaying and amplify and forward relaying in the Gaussian noise, obtaining their respective achievable rate regions, outer bounds and relative performance under different SNRs and relay geometries. Index Terms bi-directional communication, achievable rate regions, decode and forward, amplify and forward, multiple relays Sang Joon Kim, Natasha Devroye and Vahid Tarokh are with the School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138. Emails: [email protected], [email protected], [email protected]. This research is supported in part by NSF grant number ACI-0330244 and ARO MURI grant number W911NF-07-1-0376. This work was supported in part by the Army Research Office,under the MURI award No. N00014-01-1-0859. The views expressed in this paper are those of the author alone and not of the sponsor. October 7, 2008 DRAFT 2