Optimizing Bit-Labeling of Voronoi Constellations
2026-05-06 • Information Theory
Information Theory
AI summaryⓘ
The authors created a new way to rearrange how bits are assigned to points in special mathematical shapes called $D_4$ and $E_8$ lattices to reduce errors when sending data. They kept the overall shape fixed and only changed how the points were labeled with bits. By testing different label arrangements, they found small improvements in reducing bit errors, specifically 0.1 dB better for $D_4$ and 0.5 dB for $E_8$ lattices at a certain error rate. These gains are relative to the usual labeling methods used in previous studies.
bit-to-symbol mappingroot latticesD4 latticeE8 latticebit error ratelattice constellationbasis matriceslattice gainsignal labeling
Authors
Carilyn Rumrill, David Muzzey, Connor Davis, Stephen Mackes, Dan Chew
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 $10^{-4}$.