On the Existence of Cyclic Lattice Codes

Chengpin Luo, Brian M. Kurkoski

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 f…