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.

翻译：本文介绍了陪集Bombe码，这是一种新型的多层陪集码，将极化码推广到稠密格结构。通过利用为格调制设计的非二进制码进行多层编码，并结合Voronoi成形技术，Bombe码融合了稠密格（如$D_4$）的几何优势与极化码的逼近容量特性。在加性高斯白噪声（AWGN）信道上的实验结果表明，陪集Bombe码在16-QAM调制下显著优于BICM和MLC现有最优方案。该方案在AWGN信道仿真中实现了高达0.8 dB的增益，并将块长延迟减半，同时在256比特和1024比特码字上保持了优异的比特误码率和块误码率（BER/BLER）性能。