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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.
We consider the closest lattice point problem in a distributed network setting and study the communication cost and the error probability for computing an approximate nearest lattice point, using the nearest-plane algorithm, due to Babai. Two distinc
We show that for those lattices of Voronois first kind with known obtuse superbasis, a closest lattice point can be computed in $O(n^4)$ operations where $n$ is the dimension of the lattice. To achieve this a series of relevant lattice vectors that c
We present a communication-efficient distributed protocol for computing the Babai point, an approximate nearest point for a random vector ${bf X}inmathbb{R}^n$ in a given lattice. We show that the protocol is optimal in the sense that it minimizes th
In many modern applications, large-scale sensor networks are used to perform statistical inference tasks. In this paper, we propose Bayesian methods for multiple change-point detection using a sensor network in which a fusion center (FC) can receive
Secure communication over a wiretap channel is investigated, in which an active adversary modifies the state of the channel and the legitimate transmitter has the opportunity to sense and learn the adversarys actions. The adversary has the ability to