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We consider the problem of distributed computation of the nearest latticepoint for a two dimensional lattice. An interactive model of communication isconsidered. We address the problem of reconfiguring a specific rectangularpartition, a nearest plane, or Babai, partition, into the Voronoi partition.Expressions are derived for the error probability as a function of the totalnumber of communicated bits. With an infinite number of allowed communicationrounds, the average cost of achieving zero error probability is shown to befinite. For the interactive model, with a single round of communication,expressions are obtained for the error probability as a function of the bitsexchanged. We observe that the error exponent depends on the lattice.

Communication Cost of Transforming a Nearest Plane Partition to the Voronoi Partition