English

Tail Behavior of Sphere-Decoding Complexity in Random Lattices

Information Theory 2016-11-15 v1 Computational Complexity math.IT Statistics Theory Statistics Theory

Abstract

We analyze the (computational) complexity distribution of sphere-decoding (SD) for random infinite lattices. In particular, we show that under fairly general assumptions on the statistics of the lattice basis matrix, the tail behavior of the SD complexity distribution is solely determined by the inverse volume of a fundamental region of the underlying lattice. Particularizing this result to NxM, N>=M, i.i.d. Gaussian lattice basis matrices, we find that the corresponding complexity distribution is of Pareto-type with tail exponent given by N-M+1. We furthermore show that this tail exponent is not improved by lattice-reduction, which includes layer-sorting as a special case.

Cite

@article{arxiv.0905.1215,
  title  = {Tail Behavior of Sphere-Decoding Complexity in Random Lattices},
  author = {Dominik Seethaler and Joakim Jaldén and Christoph Studer and Helmut Bölcskei},
  journal= {arXiv preprint arXiv:0905.1215},
  year   = {2016}
}

Comments

To be presented at IEEE ISIT 2009, Seoul, Korea

R2 v1 2026-06-21T12:59:37.283Z