A Linear Physical-Layer Network Coding Based Multiple Access Approach

This paper studies a linear physical-layer network coding multiple access (LPNC-MA) scheme that is capable of achieving any rate-tuples in the MAC capacity region without receiver-iterations or time-sharing. We propose to utilize q-ary irregular repeat accumulate (IRA) codes over finite integer field-s/rings and q-PAM as the underlying coded-modulation. The receiver sequentially computes M network coded (NC) message sequences, where the previously computed message sequence is used as side information in computing subsequent ones. All users' messages are then recovered by solving the computed M NC messages via the inverse of the NC coefficient matrix. A joint nested code construction and EXIT chart based code optimization method is developed, yielding near-capacity performance (within 1.1 dB the capacity limit for three users). For fading MAC, we propose a pragmatic method for identifying the network coding coefficient matrix that maximizes the mutual information. Numerical results demonstrate that the frame error rate (FER) of LPNC-MA is within a fraction of dB the outage probability of fading MAC capacity. For a relatively large number of users, it is shown that LPNC-MA remarkably outperforms NOMA-SIC and IDMA in the high spectral efficiency regime, while avoiding the big-loop receiver iteration.