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A coding lattice c and a shaping lattice ₛ forms a nested lattice code C if ₛ c. Under some conditions, C is a finite cyclic group formed by rectangular encoding. This paper presents the conditions for the existence of such C and provides some designs. These designs correspond to solutions to linear Diophantine equations so that a cyclic lattice code 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.
Luo et al. (2024) studied this question.
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