  We consider a distributed antenna system where $L$ antenna terminals (ATs)
are connected to a Central Processor (CP) via digital error-free links of
finite capacity $R_0$, and serve $L$ user terminals (UTs). This system model
has been widely investigated both for the uplink and the downlink, which are
instances of the general multiple-access relay and broadcast relay networks. In
this work we focus on the downlink, and propose a novel downlink precoding
scheme nicknamed "Reverse Quantized Compute and Forward" (RQCoF). For this
scheme we obtain achievable rates and compare with the state of the art
available in the literature. We also provide simulation results for a realistic
network with fading and pathloss with $K > L$ UTs, and show that channel-based
user selection produces large benefits and essentially removes the problem of
rank deficiency in the system matrix.
