Approximately optimal broadcasting in wireless networks

We study a wireless broadcast network, where a single source reliably communicates independent messages to multiple destinations, with the aid of relays. We propose a scheme that can achieve rates within a constant gap away from the cut-set bound. The proposed scheme operates in two steps: the inner code induces a broadcast channel with sufficient mutual information between the source and the destinations, and the outer code is basically a Marton code for broadcast channels. The inner code is constructed by lifting a scheme designed for a corresponding discrete superposition network.