2017/01/30 by Vinay A. Vaishampayan, V. A. Vaishampayan, Vaishampayan, V. A. +3 · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Cellular Automata and Applications #DNA and Biological Computing #FOS: Computer and information sciences #H.1.1 #Information Theory (cs.IT) #cs.IT #math.IT #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1701.08458
5 pages, 5 figures
arxiv created 2017/01/30 · openalex publication_date 2017/01/30 · arxiv updated 2017/01/31 · openalex created_date 2017/02/10 · openalex updated_date 2026/07/28
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.