Multilevel Coset Codes on Lattices
2026-04-07 • Information Theory
Information Theory
AI summaryⓘ
The authors introduce coset Bombe codes, a new type of code that combines advanced lattice shapes with polar codes to improve data transmission. These codes use multiple levels of coding and special shaping techniques to better fit the structure of signal spaces. Testing on noisy channels shows these codes work better than previous top methods for 16-QAM signals, offering stronger error correction and faster processing. The authors demonstrate this improvement using realistic code sizes and common noise scenarios.
coset codespolar codeslattice codesVoronoi shaping16-QAMAWGN channelbit error rateblock error ratemultilevel codingBICM
Authors
Leopold Bertholet, Chloe Makdad, Stephen Mackes, Daniel Chew, Matthew Robinson
Abstract
This work introduces coset Bombe codes, a novel class of multilevel coset codes that generalize polar codes to dense lattice structures. By leveraging multilevel coding with non-binary codes designed for the lattice modulations and making use of Voronoi shaping, Bombe codes integrate the geometric strengths of dense lattices such as $D_4$ with the capacity-approaching properties of polar codes. Experimental results in additive white Gaussian noise (AWGN) channels demonstrate that coset Bombe codes significantly outperform both BICM and MLC state-of-the-art schemes on 16-QAM. The proposed scheme simulated on AWGN achieves up to 0.8 dB of gain and reduces block size latency by half while maintaining superior bit and block error rate (BER/BLER) performance on codewords of 256 and 1024 bits.