Capacity of a class of symmetric relay networks with orthogonal components

In this study, the authors extend the concept of relay channel with orthogonal components to define a class of symmetric relay networks with orthogonal components named symmetric orthogonal relay network. In the defined network, the channels diverge from each node sender use different frequency bands whereas the channels converge to each node receiver use the same frequency band. This structure is very well understood in half-duplex transmission systems where the relays cannot send and receive at the same time or over the same frequency band. The authors show that the unicast capacity of the defined network is equal to the cut-set bound. In the achievability proof, the authors take advantage of symmetric relaying and partial decode-and-forward strategies in which each relay in the network can partially decode the message transmitted by the other relays in addition to the source message.