Single-Gaussian messages and noise thresholds for decoding low-density lattice codes

A new method for decoding low-density lattice codes is given, wherein the belief-propagation decoder messages are single Gaussian functions. Since the message can be represented by two numbers, a mean and a variance, the complexity of this decoder is lower than previous decoders, which either quantized the mixture, or used a mixture of Gaussians. The computational complexity at the check node is also lower. The performance of various code designs, under single-Gaussian decoding, is evaluated by noise thresholds. In particular, the proposed decoding algorithm has noise threshold within 0.1 dB of the quantized-message decoder, which is considerably more complex.