2014/11/02 by Линг Лиу, Liu, Ling, Yanfei Yan +5 · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · #Coding theory and cryptography #DNA and Biological Computing #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.1411.0187
openalex publication_date 2014/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose a new class of lattices constructed from polar codes, namely polar lattices, to achieve the capacity (1)/(2)log(1+\SNR) of the additive white Gaussian-noise (AWGN) channel. Our construction follows the multilevel approach of Forney et al., where we construct a capacity-achieving polar code on each level. The component polar codes are shown to be naturally nested, thereby fulfilling the requirement of the multilevel lattice construction. We prove that polar lattices are AWGN-good. Furthermore, using the technique of source polarization, we propose discrete Gaussian shaping over the polar lattice to satisfy the power constraint. Both the construction and shaping are explicit, and the overall complexity of encoding and decoding is O(Nlog N) for any fixed target error probability.