Message-passing decoding of lattices using Gaussian mixtures

A belief-propagation decoder for low-density lattice codes, which represents messages explicitly as a mixture of Gaussians functions, is given. In order to prevent the number of functions from growing as the decoder iterations progress, a method for reducing the number of Gaussians at each step is given. A squared distance metric is used, which is shown to be a lower bound on the divergence. For an unconstrained power system, comparisons are made with a quantized implementation. For a dimension 100 lattice, a loss of about 0.2 dB was found; for dimension 1000 and 10000 lattices, the difference in error rate was indistinguishable. The memory required to store the messages is substantially superior to the quantized implementation.