Leech Constellations of Construction-A Lattices

TL;DR

This paper introduces a new encoding and demapping scheme for Construction-A Voronoi lattice codes, demonstrating near-capacity performance with low complexity for Leech constellations of LDA lattices.

Contribution

It presents a novel encoding and demapping method for Construction-A Voronoi lattice codes, enabling practical implementation with near-capacity performance.

Findings

Waterfall region within 0.8 dB of Shannon capacity

Linear complexity encoding, decoding, and demapping

Effective use of dual-diagonal nonbinary LDPC codes

Abstract

The problem of communicating over the additive white Gaussian noise (AWGN) channel with lattice codes is addressed in this paper. Theoretically, Voronoi constellations have proved to yield very powerful lattice codes when the fine/coding lattice is AWGN-good and the coarse/shaping lattice has an optimal shaping gain. However, achieving Shannon capacity with these premises and practically implementable encoding algorithms is in general not an easy task. In this work, a new way to encode and demap Construction-A Voronoi lattice codes is presented. As a meaningful application of this scheme, the second part of the paper is focused on Leech constellations of low-density Construction-A (LDA) lattices: LDA Voronoi lattice codes are presented whose numerically measured waterfall region is situated at less than 0.8 dB from Shannon capacity. These LDA lattice codes are based on dual-diagonal nonbinary low-density parity-check codes. With this choice, encoding, iterative decoding, and demapping have all linear complexity in the blocklength.