Name
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 nu003e1. 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. |
Year | Venue | Field |
|---|---|---|
2018 | arXiv: Information Theory | Discrete mathematics,Lattice (order),Sphere packing,Euclidean space,Lattice (group),Probability of error,Mathematics |
DocType | Volume | Citations |
Journal | abs/1801.09796 | 0 |
PageRank | References | Authors |
0.34 | 8 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Maiara F. Bollauf | 1 | 0 | 1.01 |
| Vinay A. Vaishampayan | 2 | 367 | 43.11 |
| Sueli I. R. Costa | 3 | 21 | 8.66 |