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Low-density lattice codes (LDLCs) achieve near-capacity performance on additive white Gaussian noise (AWGN) channels. The M-Gaussian decoder is the state-of-the-art message passing decoder for LDLCs in terms of the error performance. However, this decoder has complexity O(Md-1) with messages represented by Gaussian mixtures, where d is the degree of an LDLC and M is the number of Gaussian functions for approximating each check node message. In this paper, we establish the correspondence between Gaussian functions for approximating a variable node message and points of a certain lattice. Based on this lattice viewpoint, the problem of approximating a variable node message is formulated as a lattice point enumeration (LPE) problem. Then, an LPE decoder with linear complexity O(d) is proposed. Our simulation results validate that the LPE decoder achieves almost the same error performance as the M-Gaussian decoder.

Efficient Decoder Design for Low-Density Lattice Codes From the Lattice Viewpoint