Lattice network codes over optimal lattices in low dimensions

Lattice network coding is an important building block of physical-layer network coding. The receiver is required to compute a linear combination of the source symbols belonging to a finite alphabet with an algebraic structure. In this paper, lattice network codes are constructed from lattices that have optimal packing density and the best known shaping gain in low dimensions. Using the efficient quantization functions of these optimal lattices, practical lattice network codes are constructed. Simulation results demonstrate that there is a 4 to 5 dB performance gain in comparison to the baseline lattice network code with hypercube shaping.