Message-Passing Decoding of Lattices Using Gaussian Mixtures

Abstract

A lattice decoder which represents messages explicitly as a mixture of Gaussians functions is given. In order to prevent the number of functions in a mixture from growing as the decoder iterations progress, a method for replacing N Gaussian functions with M Gaussian functions, with M < N, is given. A squared distance metric is used to select functions for combining. A pair of selected Gaussians is replaced by a single Gaussian with the same first and second moments. The metric can be computed efficiently, and at the same time, the proposed algorithm empirically gives good results, for example, a dimension 100 lattice has a loss of 0.2 dB in signal-to-noise ratio at a probability of symbol error of 10^{-5}.