Approximation du LLR pour un Décodage Multi-niveaux de Réseaux de Points Imbriqués

Multilevel coding (MLC) is a practical encoding scheme for nested lattice codes based on construction D, since it saves complexity while using a hypercube shaping. On the other hand, multistage decoding is also an efficient and practical decoding scheme for MLC provided that the underlying error correcting codes of construction D are capacity achieving, which requires a powerful soft decoder for each code. In this article, we propose an approximation of the log-likelihood ratio (LLR) used for the soft decoding of the different error correcting codes used in the nested lattices construction. This approximation is based on the von Mises distribution and achieves the same error rate performance as the exact LLR expression but with much lower complexity.