Message-Passing Decoding of Lattices Using Gaussian Mixtures

TL;DR

This paper introduces a Gaussian mixture message-passing lattice decoder that controls complexity growth and achieves near-optimal performance, demonstrated by a 0.2 dB SNR loss at very low error probability.

Contribution

It presents a novel lattice decoding method using Gaussian mixtures with an efficient merging algorithm to maintain manageable complexity.

Findings

Achieves 0.2 dB SNR loss at a symbol error probability of 10^{-5}.

Effectively controls the number of Gaussian functions during decoding.

Demonstrates good empirical performance in high-dimensional lattices.

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}.