In this work, we propose a novel sequential decoder for MIMO systems termed the Zigzag Stack decoder. The algorithm combines the search strategy of the Stack decoder with the Schnorr-Euchner zigzagging method. We show that the Zigzag Stack provides ML performance with a reduced complexity compared to the original Stack decoder and a complexity reduction of 40% in average over the commonly used sphere decoder.

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 Z lattices.

Integer Forcing (IF) architecture has been recently proposed to design linear receivers in MIMO systems. Research works show the promise of this architecture from a capacity achieving perspective. However, it is not totally understood how to select IF coefficient matrix and if the promised theoretical gain of the resulting receivers is attainable in practical settings. We try in this work to fill the gap between theory and practice: we propose algorithms to select optimal IF receiver parameters that lead to the maximization of the total achievable rate. We propose an implementation of an IF-based MIMO system considering a practical scenario where lattice codes are used. Experimental studies are carried out to evaluate the error rate performance of the proposed algorithms and compare them to traditional linear receivers. Our proposed implementation shows that the theoretical potential of the IF receivers is achievable even with finite-length lattice codes.