Optimizing Bit-Labeling of Voronoi Constellations
This provides a modest improvement in lattice-based communication systems, but is incremental as it only optimizes bit-labeling while holding other factors constant.
The authors optimize the bit-to-symbol mapping for D4 and E8 root lattices to improve bit error rate, achieving 0.1 dB gain for D4 and 0.5 dB gain for E8 at BER 10^{-4} compared to standard bases.
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 $10^{-4}$.