On the Existence of Cyclic Lattice Codes
<|reference_start|>On the Existence of Cyclic Lattice Codes: A coding lattice $\Lambda_c$ and a shaping lattice $\Lambda_s$ forms a nested lattice code $\mathcal{C}$ if $\Lambda_s \subseteq \Lambda_c$. Under some conditions, $\mathcal{C}$ is a finite cyclic group formed by rectangular encoding. This paper presents the conditions for the existence of such $\mathcal{C}$ and provides some designs. These designs correspond to solutions to linear Diophantine equations so that a cyclic lattice code $\mathcal C$ of arbitrary codebook size $M$ can possess group isomorphism, which is an essential property for a nested lattice code to be applied in physical layer network relaying techniques such as compute and forward.<|reference_end|>
@article{luo2024on,
    title={On the Existence of Cyclic Lattice Codes},
    author={Chengpin Luo and Brian M. Kurkoski},
    journal={arXiv preprint arXiv:2402.18094},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.18094},
    primaryClass={cs.IT math.IT}
}