Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.18094 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916239705636864 |
|---|---|
| author | Luo, Chengpin Kurkoski, Brian M. |
| author_facet | Luo, Chengpin Kurkoski, Brian M. |
| contents | A coding lattice $Λ_c$ and a shaping lattice $Λ_s$ forms a nested lattice code $\mathcal{C}$ if $Λ_s \subseteq Λ_c$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18094 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Existence of Cyclic Lattice Codes Luo, Chengpin Kurkoski, Brian M. Information Theory A coding lattice $Λ_c$ and a shaping lattice $Λ_s$ forms a nested lattice code $\mathcal{C}$ if $Λ_s \subseteq Λ_c$. 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. |
| title | On the Existence of Cyclic Lattice Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2402.18094 |