On the capacity region of semi-deterministic Multiple-Access-Relay-Networks

In this paper, we introduce a generalization of the multiple-access-relay-channel (MARC) called multiple-access-relay-network (MARN). In the proposed network, there are many transmitters, many relays and one receiver. The MARC model was first introduced by Kramer and consists of many transmitters, one receiver and only one relay.We also define semi-deterministic MARN, in which the output of the link between each transmitter and each relay is a deterministic function of the transmitter´s input. We first obtain an achievable rate region for MARN by considering partial decode-and-forward (PDF) strategy at the relays. Then we show that in semi-deterministic MARN, the proposed achievable rate region yields the capacity region.We also prove that the region obtained using PDF strategy subsumes the region obtained by Kramer for MARC. In our coding scheme, each transmitter´s message is partitioned into different parts. These parts are sent to all relays and also to the receiver. Each relay uses Partial Decode-and-Forward (PDF) strategy to decode its own share of each transmitter´s message. It then forwards a copy of all decoded sequences to the receiver. In the proof, we take advantage of regular encoding/backward decoding strategy at the receiver, and also the proof of Mutiple-Access-Channel (MAC)´s capacity region is utilized to analyze the probability of error at relays and the receiver.