最近平面划分到Voronoi划分的通信代价
Communication Cost of Transforming a Nearest Plane Partition to the Voronoi Partition
摘要：
本文研究二维的格点最近格点的分布式计算问题。被认为是一个互动的沟通模式。我们解决的问题，重新配置一个特定的矩形分区，最近的平面，或Babai，分区，到Voronoi分区。表达式推导出的错误概率作为通信位的总数的函数。与无限数量的允许的通信轮，实现零错误概率的平均成本是有限的。对于交互式模型，与一个单一的一轮的通信，表达式获得的错误概率作为交换的位的函数。我们观察到，误差指数取决于晶格。
英文摘要：
We consider the problem of distributed computation of the nearest lattice point for a two dimensional lattice. An interactive model of communication is considered. We address the problem of reconfiguring a specific rectangular partition, a nearest plane, or Babai, partition, into the Voronoi partition. Expressions are derived for the error probability as a function of the total number of communicated bits. With an infinite number of allowed communication rounds, the average cost of achieving zero error probability is shown to be finite. For the interactive model, with a single round of communication, expressions are obtained for the error probability as a function of the bits exchanged. We observe that the error exponent depends on the lattice.
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