  We present a communication-efficient distributed protocol for computing the
Babai point, an approximate nearest point for a random vector ${\bf
X}\in\mathbb{R}^n$ in a given lattice. We show that the protocol is optimal in
the sense that it minimizes the sum rate when the components of ${\bf X}$ are
mutually independent. We then investigate the error probability, i.e. the
probability that the Babai point does not coincide with the nearest lattice
point. In dimensions two and three, this probability is seen to grow with the
packing density. For higher dimensions, we use a bound from probability theory
to estimate the error probability for some well-known lattices. Our
investigations suggest that for uniform distributions, the error probability
becomes large with the dimension of the lattice, for lattices with good packing
densities. We also consider the case where $\mathbf{X}$ is obtained by adding
Gaussian noise to a randomly chosen lattice point. In this case, the error
probability goes to zero with the lattice dimension when the noise variance is
sufficiently small. In such cases, a distributed algorithm for finding the
approximate nearest lattice point is sufficient for finding the nearest lattice
point.
