Communication-Efficient Search for an Approximate Closest Lattice Point
Abstract
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. Assuming a triangular special basis for the lattice, we develop communication-efficient protocols for computing the approximate lattice point and determine the communication cost for lattices of dimension n>1. Based on available parameterizations of reduced bases, we determine the error probability of the nearest plane algorithm for two dimensional lattices analytically, and present a computational error estimation algorithm in three dimensions. For dimensions 2 and 3, our results show that the error probability increases with the packing density of the lattice.
Cite
@article{arxiv.1801.09796,
title = {Communication-Efficient Search for an Approximate Closest Lattice Point},
author = {Maiara F. Bollauf and Vinay A. Vaishampayan and Sueli I. R. Costa},
journal= {arXiv preprint arXiv:1801.09796},
year = {2018}
}