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

Abstract

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 $O(M^{d-1})$ 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.

Keywords

• Low-density lattice codes
• message passing
• decoding complexity
• lattice point enumeration