Improvements in closest point search based on dual HKZ-bases

Improvements in closest point search based on dual HKZ-bases

In this paper we review the technique to solve the CVP based on dual HKZ-bases by J. Blömer [4]. The technique is based on the transference theorems given by Banaszczyk [3] which imply some necessary conditions on the coefficients of the closest vectors with respect to a basis whose dual is HKZ reduced. Recursively, starting with the last coefficient, intervals of length i can be derived for th...

Closest point search in lattices

In this semitutorial paper, a comprehensive survey of closest point search methods for lattices without a regular structure is presented. The existing search strategies are described in a unified framework, and differences between them are elucidated. An efficient closest point search algorithm, based on the Schnorr–Euchner variation of the Pohst method, is implemented. Given an arbitrary point...

Closest Point Search in High Dimensions

The problem of nding the closest point in high-dimensional spaces is common in computational vision. Unfortunately, the complexity of most existing search algorithms , such as k-d tree and R-tree, grows exponentially with dimension, making them impractical for di-mensionality above 15. In nearly all applications, the closest point is of interest only if it lies within a user speciied distance. ...

The Dual - Bootstrap Iterative Closest Point Algorithm

Communication-Efficient Search for an Approximate Closest Lattice Point

We consider the problem of finding the closest lattice point to a vector in n-dimensional Euclidean space when each component of the vector is available at a distinct node in a network. Our objectives are (i) minimize the communication cost and (ii) obtain the error probability. The approximate closest lattice point considered here is the one obtained using the nearest-plane (Babai) algorithm. ...