  Lattice codes are elegant and powerful structures that not only can achieve
the capacity of the AWGN channel but are also a key ingredient to many
multiterminal schemes that exploit linearity properties. However, constructing
lattice codes that can realize these benefits with low complexity is still a
challenging problem. In this paper, efficient encoding and decoding algorithms
are proposed for multilevel binary LDPC lattices constructed via Construction
D' whose complexity is linear in the total number of coded bits. Moreover, a
generalization of Construction D' is proposed that relaxes some of the nesting
constraints on the parity-check matrices of 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
decoding is comparable to that of polar lattices and close to that of
low-density lattice codes (LDLC) on the power-unconstrained AWGN channel.
