Low-Complexity Multilevel LDPC Lattices and a Generalization of Construction D′

We propose efficient encoding and decoding algorithms for Construction D' multilevel LDPC lattices whose complexity is linear in the total number of coded bits. Moreover, we propose a generalization of Construction D' that relaxes some of the nesting constraints on the component codes, leading to a simpler and improved design. Based on this construction, low-complexity multilevel LDPC lattices are designed whose performance under multistage lattice decoding is comparable to that of polar lattices on the power-unconstrained AWGN channel.