Multilevel lattices based on spatially-coupled LDPC codes with applications

We propose a class of lattices constructed using Construction D where the underlying linear codes are nested binary spatially-coupled low-density parity-check codes (SC-LDPC) codes with uniform left and right degrees. By leveraging recent results on the optimality of spatially-coupled codes for binary input memoryless channels and Forney et al.´s earlier results on the optimality of construction D, we show that the proposed lattices achieve the Poltyrev limit under multistage belief propagation decoding. Lattice codes constructed from these lattices are shown to provide excellent performance for the three user symmetric interference channel. They can also be naturally used in applications such as integer-forcing and compute-and-forward.