Finding the closest lattice point by iterative slicing

Naftali Sommer*, Meir Feder, Ofir Shalvi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Most of the existing methods that are used to solve the closest lattice point problem are based on an efficient search of the lattice points. In this paper a novel alternative approach is suggested where the closest point to a given vector is found by calculating which Voronoi cell contains this vector in an iterative manner. Each iteration is made of simple "slicing" operations, using a list of the Voronoi relevant vectors that define the basic Voronoi cell of the lattice. The algorithm is guaranteed to converge to the closest lattice point in a finite number of steps. The method is suitable, for example, for decoding of multi-input multi-output (MIMO) communication problems. The average computational complexity of the proposed method is comparable to that of the efficient variants of the sphere decoder, but its computational variability is smaller.

Original languageEnglish
Pages (from-to)715-731
Number of pages17
JournalSIAM Journal on Discrete Mathematics
Issue number2
StatePublished - 2009


  • Closest neighbor
  • Closest point search
  • Lattice
  • Lattice codes
  • Lattice decoding
  • Lattice quantization
  • Voronoi relevant vectors


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