Achievable rate region for broadcast-relay networks with two cooperative relays

The authors consider the problem of broadcast-relay-networks with two cooperative relays. There are a transmitter, two relays and two receivers in the network. The message of the transmitter intended to the receivers has common and private parts. The relays fully cooperate with each other and with the transmitter to send the common part of the message, whereas the private parts of the message are sent through the direct links between the transmitter and receivers. The authors found an achievable rate region for this network by using the symmetric relaying strategy. In this strategy, each relay completely decodes the message of other relay. In the proof the authors took advantage of regular encoding/sliding window decoding at relays and simultaneous backward decoding analysis at receivers. Marton´s broadcast code construction is used at the transmitter to split the rate between the users. Three special cases of achievable rate region are shown: (i) Kramer´s achievable rate region for broadcast relay channel; (ii) Ghabeli´s achievable rate for symmetric two-relay network; and (iii) Marton´s achievable rate region for broadcast channel with common message. The additive white Gaussian noise model is also considered and the achievable rate region of Gaussian network is discussed.