Optimal coefficients for channel-coded linear physical layer network coding

This paper investigates the linear network coding map in a Physical-layer Network Coding (PNC) operated two-way relay network. To realize the full potential of Physical-layer Network Coding in high SNR regimes, we need to use high-order signaling beyond BPSK/QPSK. In a PNC system with high-order signaling, we can have many different choices for the network coding (NC) map. For linear network coding, the network-coding map is realized by coefficients corresponding to the weights of the linearly-combined network-coded message. Prior work on channel-coded linear PNC adopted the same network-coding coefficients as in non-channel-coded linear PNC. We find that the optimal coefficients for such uncoded systems are far from optimal for coded systems. We also show that the coefficients that maximize the computation rate in the “compute-and-forward” framework, which adopts nested lattice codes, are near optimal for linear PNC that adopts the LDPC codes.