Belief-Propagation Decoding of Lattices Using Gaussian Mixtures

TL;DR

This paper introduces a belief-propagation decoder for low-density lattice codes that uses Gaussian mixtures to represent messages, with an efficient reduction algorithm, achieving comparable error rates to previous methods but with less storage.

Contribution

It presents a novel Gaussian mixture reduction algorithm for belief-propagation decoding of lattices, improving efficiency and storage over prior quantization-based methods.

Findings

Error rates are similar to previous decoders at high dimensions.

The Gaussian-mixture decoder has a small 0.2 dB loss in noise threshold.

It requires significantly less storage for messages.

Abstract

A belief-propagation decoder for low-density lattice codes is given which represents messages explicitly as a mixture of Gaussians functions. The key component is an algorithm for approximating a mixture of several Gaussians with another mixture with a smaller number of Gaussians. This Gaussian mixture reduction algorithm iteratively reduces the number of Gaussians by minimizing the distance between the original mixture and an approximation with one fewer Gaussians. Error rates and noise thresholds of this decoder are compared with those for the previously-proposed decoder which discretely quantizes the messages. The error rates are indistinguishable for dimension 1000 and 10000 lattices, and the Gaussian-mixture decoder has a 0.2 dB loss for dimension 100 lattices. The Gaussian-mixture decoder has a loss of about 0.03 dB in the noise threshold, which is evaluated via Monte Carlo density evolution. Further, the Gaussian-mixture decoder uses far less storage for the messages.