An achievable rate region for Broadcast-Relay Networks with partial cooperation between relays

In this paper, we consider a different strategy for broadcast-relay-networks (BRN) with two relays. There are a transmitter, two relays and two receivers in this network. The message of the transmitter intended to the receivers, has both common and private parts. The relays partially cooperate with each other and with the transmitter to send the common part of the message. The private parts of the message are sent to the corresponding receiver by the cooperation of the corresponding relay. We propose an achievable rate region for this network. In the proof, we take advantage of regular encoding/sliding window decoding at relays and simultaneous backward decoding analysis at receivers. The partial cooperation between relays is managed by symmetric relaying strategy. We will show that two special cases of our achievable rate region are: 1) Kramer's achievable rate region for broadcast-relay-channel (BRC), 2) Salehkalaibar's achievable rate region for broadcast-relay-network (BRN), by the assumption that the private parts are relaxed in these two models. This assumption is suitable for comparison of the BC models, because the main point in broadcasting is managing the common parts of the message. The private parts are defined according to application of the network. Obviously, the proposed achievable rate region includes Ghabeli's rate for the symmetric two-relay network.