Lattice decoding for the compute-and-forward protocol

Abstract—In this work we focus exclusively on the Compute-and-Forward (C&F) protocol as a channel coding-based ap-proach for Physical Layer Network Coding. The Core principle of this relaying strategy is based on using Nested Lattice Codes. The source nodes in a relay network encode their messages into lattice codewords and transmit them to the relay. The latter receives a noisy mixing of these codewords and decodes an integer linear combination of them for sequential transmission. To the best of our knowledge, all existent works related to the Compute-and-Forward protocol study only its theoretical limits and no experimental analysis has been proposed so far. Our contribution through this work concerns a plethora of practical aspects, related to lattice decoding for the C&F, that need to be solved to achieve the promising potential of this strategy. We propose practical decoding approaches and investigate the achieved diversity order and identify the relevant parameters that may influence it. We provide simulation results to compare the performance of the different proposed decoding approaches and to link theoretical results with practical aspects