# Information Properties of a Random Variable Decomposition through Lattices

@article{Meneghetti2022InformationPO, title={Information Properties of a Random Variable Decomposition through Lattices}, author={F{\'a}bio C. C. Meneghetti and Henrique K. Miyamoto and Sueli Irene Rodrigues Costa}, journal={ArXiv}, year={2022}, volume={abs/2211.03477} }

A full-rank lattice in the Euclidean space is a discrete set formed by all integer linear combinations of a basis. Given a probability distribution on R n , two operations can be induced by considering the quotient of the space by such a lattice: wrapping and quantization. For a lattice Λ, and a fundamental domain D which tiles R n through Λ, the wrapped distribution over the quotient is obtained by summing the density over each coset, while the quantized distribution over the lattice is deﬁned…

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