Tail behavior of sphere-decoding complexity in random lattices

Authors:
D. Seethaler;J. Jaldén;C. Studer;H. Bölcskei
Affiliations:
Communication Technology Laboratory, ETH Zurich, Zurich, Switzerland;Institute of Communications and Radio-Frequency Engineering, Vienna University of Technology, Vienna, Austria;Communication Technology Laboratory, ETH Zurich, Zurich, Switzerland;Communication Technology Laboratory, ETH Zurich, Zurich, Switzerland
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Year:
2009

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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 N × M, 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.