Multilevel LDPC Lattices with Efficient Encoding and Decoding and a Generalization of Construction D'
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Lattice codes are elegant and powerful structures that not only can achieve the capacity of the AWGN channel but also are 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 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 and close to that of conventional (non-lattice) coded modulation schemes on the power-constrained AWGN channel.
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