Max-product algorithm for low density lattice codes

A max-product algorithm for approximating maximum-likelihood lattice decoding of low density lattice codes is derived, operating directly in the Euclidean space. First we derive the max-product algorithm for continuous channels by taking a factor graph based approach. Then, for the additive white Gaussian noise channel we show the relation between the sum-product and max-product algorithms for low density lattice codes. In both algorithms the messages consist of the same Gaussians. While in the sum-product algorithm we sum the Gaussians in each message, for the max-product we take the maximal envelope of these Gaussians. Finally, we extend the parametric approach to efficiently implement the max-product algorithm, and show decrease in the word error rate (WER).