Well-rounded twists of ideal lattices from real quadratic fields

Damir, Mohamed Taoufiq; Karpuk, David

doi:10.1016/j.jnt.2018.09.017

Cited by 6 publications

(11 citation statements)

References 20 publications

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“…This shows that the space of WR lattices is not a full-dimensional space in S N , and in particular it has zero measure. The following figure illustrates S 2 and W 2 , the sets of similarity classes and well-rounded planar lattices [8].…”

Section: General Background On Latticesmentioning

confidence: 99%

Bases of minimal vectors in tame lattices

Damir

Mantilla-Soler²

2022

Acta Arith.

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Section: General Background On Latticesmentioning

confidence: 99%

Bases of minimal vectors in tame lattices

Damir

Mantilla-Soler²

2022

Acta Arith.

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“…Strongly well-rounded lattices, are defined as lattices having a basis consisting of vectors of minimum norm, which in our context is equal to 1. Well-rounded lattices have been studied generally [9], [21], and also for applications such as coding for wiretap Gaussian and fading channels [10], [14].…”

Section: Some Observations and Analysis Of The Datamentioning

confidence: 99%

On Communication for Distributed Babai Point Computation

Bollauf¹,

Vaishampayan²,

Costa³

2020

Preprint

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We present a communication-efficient distributed protocol for computing the Babai point, an approximate nearest point for a random vector X ∈ R n in a given lattice. We show that the protocol is optimal in the sense that it minimizes the sum rate when the components of X are mutually independent.We then investigate the error probability, i.e. the probability that the Babai point does not coincide with the nearest lattice point. In dimensions two and three, this probability is seen to grow with the packing density. For higher dimensions, we use a bound from probability theory to estimate the error probability for some well-known lattices. Our investigations suggest that for uniform distributions, the error probability becomes large with the dimension of the lattice, for lattices with good packing densities.We also consider the case where X is obtained by adding Gaussian noise to a randomly chosen lattice point. In this case, the error probability goes to zero with the lattice dimension when the noise variance is sufficiently small. In such cases, a distributed algorithm for finding the approximate nearest lattice point is sufficient for finding the nearest lattice point.

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“…A well-rounded twist of a lattice is defined in [3]. A method for computing all well-rounded twists of a given ideal lattice I of a real quadratic field K is also presented in this paper.…”

Section: Introductionmentioning

confidence: 99%