  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.
