An Algorithm to Compute the Nearest Point in the Lattice $A_{n}^*$

Details An Algorithm to Compute the Nearest Point in the Lattice $A_{n}^*$ An Algorithm to Compute the Nearest Point in the Lattice $A_{n}^*$

2008-01-09

arxiv.org/abs/0801.1364v2

IEEE Transactions on Information Theory, Vol. 54, No. 9, pp 4378-4381, Sept. 2008

Computer Science

Information Theory

3 pages

Scientific paper

10.1109/TIT.2008.928280

The lattice $A_n^*$ is an important lattice because of its covering properties in low dimensions. Clarkson \cite{Clarkson1999:Anstar} described an algorithm to compute the nearest lattice point in $A_n^*$ that requires $O(n\log{n})$ arithmetic operations. In this paper, we describe a new algorithm. While the complexity is still $O(n\log{n})$, it is significantly simpler to describe and verify. In practice, we find that the new algorithm also runs faster.

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