Complex low-density lattice codes designed for ISI channels via spatial coupling

Complex low-density lattice codes (LDLC) designed via spatial coupling for inter-symbol interference (ISI) channels are proposed in this paper. A complex node-by-node belief propagation (BP) decoding algorithm is derived. To improve the BP threshold lattice codes are directly constructed in the Euclidean space via spatial coupling technique. A semi-analytical density evolution method is used to search the BP threshold as well as elements of the parity matrix. Voronoi shaping operation is employed to utilize the potential nominal coding gain and the shaping gain. Simulation results show that error performance of complex spatially-coupled LDLC codes is less than ldB from capacity at dimension 10,000.