Efficient decoding algorithms for the compute-and-forward strategy

We address in this paper decoding aspects of the Compute-and-Forward (CF) physical-layer network coding strategy. Under the CF framework, encoders use a special class of nested lattice codes and decoders are based on suboptimal minimum distance decoding of unknown performance gap with respect to optimal decoders. In this work, we develop and assess the performance of novel decoding algorithms for CF operating in the multiple access channel. Starting with the Gaussian channel, we investigate the maximum a posteriori (MAP) decoder. We derive a novel MAP decoding metric and develop practical decoding algorithms shown numerically to outperform the original one. For the fading channel, we analyze the ML decoder for integer-valued lattices and develop a novel Diophantine approximation-based near-ML decoding algorithm shown numerically to outperform the original CF decoder in the 1-D case using $\mathbb{Z}$ lattices.