The three/two Gaussian parametric LDLC decoder

Low density lattice codes (LDLC) can be decoded efficiently using iterative decoding, and approach the capacity of the AWGN channel. In the iterative LDLC decoder the messages are Gaussian mixtures. In any implementation, the Gaussian mixtures must be approximated. This work describes a three/two Gaussian parametric LDLC decoder. Internally at the variable node the periodic Gaussian mixtures are approximated with three or two Gaussians, while the messages between nodes are single Gaussians. The proposed approximation is more accurate than the previously-proposed approximation. Numerical results shows that for moderate dimension, e.g. n = 1, 000, the two Gaussian approximation is sufficient for accurate performance. But for large dimension, e.g. n = 10, 000, three Gaussians are needed.