Align-and-forward relaying for two-hop erasure broadcast channels

We consider the problem of broadcast over wireless erasure networks. To understand the challenges and opportunities of these setups, we study a two-hop erasure broadcast channel consisting of a single source, two relays, and two destinations desiring independent messages. In our network, no transmitter has channel state knowledge of erasures on outgoing links (i.e., no CSIT): The source has no knowledge of any channel state, each relay only has knowledge of the channel states of its incoming link, and destinations are provided with full channel knowledge. We propose a scheme, referred to as Align-and-Forward, that exploits the (unknown) common subspace of received signals at the relays, which results from the source-to-relay broadcast, in order to minimize the dimension of the interference subspace at each destination. We show that Align-and-Forward outperforms available alternative schemes in terms of sum-rate. We also present new outer-bounds and demonstrate the optimality of Align-and-Forward in certain regimes.