  We study 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 $K$ user terminals (UTs). We contribute to the
subject in the following ways: 1) for the uplink, we apply the "Compute and
Forward" (CoF) approach and examine the corresponding system optimization at
finite SNR; 2) For the downlink, we propose a novel precoding scheme nicknamed
"Reverse Compute and Forward" (RCoF); 3) In both cases, we present
low-complexity versions of CoF and RCoF based on standard scalar quantization
at the receivers, that lead to discrete-input discrete-output symmetric
memoryless channel models for which near-optimal performance can be achieved by
standard single-user linear coding; 4) For the case of large $R_0$, we propose
a novel "Integer Forcing Beamforming" (IFB) scheme that generalizes the popular
zero-forcing beamforming and achieves sum rate performance close to the optimal
Gaussian Dirty-Paper Coding.
  The proposed uplink and downlink system optimization focuses specifically on
the ATs and UTs selection problem. We present low-complexity ATs and UTs
selection schemes and demonstrate, through Monte Carlo simulation in a
realistic environment with fading and shadowing, that the proposed schemes
essentially eliminate the problem of rank deficiency of the system matrix and
greatly mitigate the non-integer penalty affecting CoF/RCoF at high SNR.
Comparison with other state-of-the art information theoretic schemes, such as
"Quantize reMap and Forward" for the uplink and "Compressed Dirty Paper Coding"
for the downlink, show competitive performance of the proposed approaches with
significantly lower complexity.
