Multilevel Coset Codes on Lattices

TL;DR

This paper introduces coset Bombe codes, a new multilevel lattice coding scheme that combines geometric lattice properties with polar code advantages, achieving significant performance gains in AWGN channels.

Contribution

It proposes a novel class of multilevel coset codes called coset Bombe codes, generalizing polar codes for dense lattice structures with improved performance.

Findings

Achieves up to 0.8 dB gain over existing schemes in AWGN channels.

Reduces block size latency by half while maintaining superior error rates.

Significantly outperforms BICM and MLC schemes on 16-QAM.

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.