  We study a wireless broadcast network, where a single source reliably
communicates independent messages to multiple destinations, with the aid of
relays and cooperation between destinations. The wireless nature of the medium
is captured by the broadcast nature of transmissions as well as the
superposition of all transmit signals plus independent Gaussian noise at the
received signal at any radio. We propose a scheme that can achieve rate tuples
within a constant gap away from the cut-set bound, where the constant is
independent of channel coefficients and power constraints.
  The proposed scheme operates in two steps. The inner code, in which the
relays perform a quantize-and-encode operation, is constructed by lifting a
scheme designed for a corresponding discrete superposition network. The outer
code is a Marton code for the non-Gaussian vector broadcast channel induced by
the relaying scheme, and is constructed by adopting a ``receiver-centric''
viewpoint.
