Bi-directional half-duplex relaying protocols

The bi-directional relay channel is the natural extension of a three-terminal relay channel where node a transmits to node b with the help of a relay r to allow for two-way communication between nodes a and b. That is, in a bi-directional relay channel, a and b wish to exchange independent messages over a shared channel with the help of a relay r. The rates at which this communication may reliably take place depend on the assumptions made on the relay processing abilities. We overview information theoretic limits of the bi-directional relay channel under a variety of conditions, before focusing on half-duplex nodes in which communication takes place in a number of temporal phases (resulting in protocols), and nodes may forward messages in four manners. The relay-forwarding considered are: Amplify and forward (AF), decode and forward (DF), compress and forward (CF), and mixed forward. The last scheme is a combination of CF in one direction and DF in the other. We derive inner and outer bounds to the capacity region of the bi-directional relay channel for three temporal protocols under these four relaying schemes. The first protocol is a two phase protocol where a and b simultaneously transmit during the first phase and the relay r alone transmits during the second. The second protocol considers sequential transmissions from a and b followed by a transmission from the relay while the third protocol is a hybrid of the first two protocols and has four phases. We provide a comprehensive treatment of protocols in Gaussian noise, obtaining their respective achievable rate regions, outer bounds, and their relative performance under different SNR and relay geometries.