On the capacity of erasure relay channel: multi-relay case

We consider here a single sender-destination multi-relay channel. The links connecting the nodes are supposed to be erasure where symbols are received correctly without any error, or lost. We consider that the nodes are not able to use any interference cancellation mechanism. The interference might be suppressed through using separated physical channel or thought a time-sharing mechanism. This model is realistic for many practical scenarios in the context of wireless networks. In previous works, the capacity region of broadcast erasure channels as well as the capacity of the single-sender relay channel (under degraded and non-degraded hypothesis) has been derived. This paper extends the previous results to the more general case of multi-relay channels. We derive the cut-set bound for a general (stationary ergodic) multi-relay erasure channel, and we show that it can be reached through a practical linear coding scheme based on MDS codes.