  This paper presents a physical layer network coding (PNC) approach for
network MIMO (N-MIMO) systems to release the heavy burden of backhaul load. The
proposed PNC approach is applied for uplink scenario in binary systems, and the
design guideline serves multiple mobile terminals (MTs) and guarantees
unambiguous recovery of the message from each MT. We present a novel PNC design
criterion first based on binary matrix theories, followed by an adaptive
optimal mapping selection algorithm based on the proposed design criterion. In
order to reduce the real-time computational complexity, a two-stage search
algorithm for the optimal binary PNC mapping matrix is developed. Numerical
results show that the proposed scheme achieves lower outage probability with
reduced backhaul load compared to practical CoMP schemes which quantize the
estimated symbols from a log-likelihood ratio (LLR) based multiuser detector
into binary bits at each access point (AP).
