Efficient Demodulation for Coset Codes on Lattices
Abstract
Lattice constellations can provide significant coding and shaping gains over traditional quadrature amplitude modulations (QAMs), but have not been widely adopted due to the high implementation complexity of modulation, demodulation, and decoding. Voronoi constellations (VCs) enable an efficient modulation map that achieves shaping gain using the Voronoi cell of a lattice. Multilevel coset codes (MLCCs) are a recently proposed coded modulation scheme for VCs that realizes more efficient decoding. However, MLCCs still suffer from a soft demodulation complexity of O(d2sd) for a d-dimensional lattice with spectral efficiency s bits per real dimension. In this paper, we propose fast quantize-walk demodulation (FQWD), an efficient demodulation scheme for MLCCs that reduces the complexity to O(sd2d). Our strategy utilizes novel radial projections onto the Voronoi cells of the D4 and E8 lattices. Experimental results demonstrate that FQWD has only negligible loss in block error rate (BLER) relative to maximum likelihood demodulation under the additive white Gaussian noise (AWGN) channel. Using FQWD, we simulate MLCCs on higher-dimensional lattices with s>2 bits per dimension under AGWN for the first time, achieving BLER gains over multilevel polar codes on QAMs of up to 0.6 dB for the D4 lattice and 1.2 dB for E8.
Related
- Coset Lifted Product Codes: Constructing Quantum LDPC Codes from Non-Normal Subgroup Actions
- Efficient Perturbation-Based SC Decoding for Long Polar Codes
- Chordal Codes: Code Construction and Efficient Gaussian-Elimination Decoding
- Efficient construction of subspace design codes over constant alphabet
- Invariant means, coset correct means and the Hahn-Banach Theorem
BibTeX
@misc{makdad2026efficient,
title = {{Efficient Demodulation for Coset Codes on Lattices}},
author = {Chloe Makdad and Leopold Bertholet and Mairead Cummins and Stephen Mackes and Matthew Robinson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03807},
eprint = {2610.03807},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03807},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Efficient Demodulation for Coset Codes on Lattices
AU - Chloe Makdad
AU - Leopold Bertholet
AU - Mairead Cummins
AU - Stephen Mackes
AU - Matthew Robinson
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.03807
UR - https://arxiv.org/abs/2610.03807
AB - Lattice constellations can provide significant coding and shaping gains over traditional quadrature amplitude modulations (QAMs), but have not been widely adopted due to the high implementation complexity of modulation, demodulation, and decoding. Voronoi constellations (VCs) enable an efficient modulation map that achieves shaping gain using the Voronoi cell of a lattice. Multilevel coset codes (MLCCs) are a recently proposed coded modulation scheme for VCs that realizes more efficient decoding. However, MLCCs still suffer from a soft demodulation complexity of O(d2^sd) for a d-dimensional lattice with spectral efficiency s bits per real dimension. In this paper, we propose fast quantize-walk demodulation (FQWD), an efficient demodulation scheme for MLCCs that reduces the complexity to O(sd2^d). Our strategy utilizes novel radial projections onto the Voronoi cells of the D_4 and E_8 lattices. Experimental results demonstrate that FQWD has only negligible loss in block error rate (BLER) relative to maximum likelihood demodulation under the additive white Gaussian noise (AWGN) channel. Using FQWD, we simulate MLCCs on higher-dimensional lattices with s>2 bits per dimension under AGWN for the first time, achieving BLER gains over multilevel polar codes on QAMs of up to 0.6 dB for the D_4 lattice and 1.2 dB for E_8.
ER -