Low-complexity PHY-layer network coding for two-way compute-and-forward relaying

We present a novel low-complexity technique that obtains the Physical-Layer Network Coding (PNC) equation coefficient vectors for the two-way relay channel when Compute-and-Forward is employed. The proposed method is based on pre-computed look-up tables that are used for all channel realizations. It is shown that the size of the look-up tables can be made small by taking into account the statistics of the channel coefficients as well as power and performance specifications. Moreover, a low-complexity algorithm is developed for efficient real-time selection of the equation coefficient vectors using the instantaneous channel coefficients and the look-up tables. Although the method may at times exclude some candidate vectors from the search space, simulation results indicate that the effect on the achievable computation rate at the relay is very small. Hence, significant complexity reduction is achieved, while the computation rate remains extremely close to the optimal value.