Optimizing Bit-Labeling of Voronoi Constellations

TL;DR

This paper introduces a new search method and metric for optimizing bit-to-symbol mappings in lattice constellations, achieving notable BER improvements for D4 and E8 lattices.

Contribution

It presents a novel basis matrix search technique that enhances bit error rate performance in lattice-based constellations.

Findings

0.1 dB gain in D4 BER at 10^{-4}

0.5 dB gain in E8 BER at 10^{-4}

Optimized basis matrices outperform standard bases

Abstract

We define a novel search method and performance metric as a technique for optimizing the bit-to-symbol map of the $D_4$ and $E_8$ root lattices in reference to bit error rate. We hold other sources of lattice gain constant by fixing the lattice constellation, and consider basis matrices that permute the integer labelings of the lattice points. After searching the possible basis matrices for $D_4$ and $E_8$, we found 0.1 dB of gain in $D_4$ bit error rate curves, and 0.5 dB of gain in $E_8$ compared to the standard bases commonly used in literature at a BER of $10^{-4}$.