Reliability-Based Decoding of Complex Low-Density Lattice Codes

This paper proposes a low-complexity decoding algorithm for complex low-density lattice codes (CLDLC). The key is a method to approximate an infinite complex Gaussian mixture that occurs at the variable node of the belief propagation (BP) decoder. We define the reliability of check-to-variable messages and a threshold function to determine the number of complex Gaussian functions to use in the approximation. This allows the number of Gaussians in the approximation to be adaptively selected depending upon its reliability. By using the minimum number of Gaussians needed for an accurate approximation, the complexity of the decoder can be significantly reduced. The reliability is based on a likelihood function, and we form an upper bound on the Kullback-Leibler (KL) divergence to find the threshold function via linear regression. The approximation based on reliability of each message can reduce the complexity to O(n · t · 1.35 d−1 ) at high volume-to-noise ratio (VNR), where n is the lattice dimension, d is the degree of the inverse generator matrix, and t is the number of iterations. This algorithm provides higher performance and lower complexity compared to previously proposed approximation algorithms. and provides higher performance and lower complexity compared to previously proposed approximation algorithms.