Tail behavior of sphere-decoding complexity in random lattices


Dominik Seethaler, Joakim JaldĂ©n, Christoph Studer, and Helmut Bölcskei


Proc. of IEEE International Symposium on Information Theory (ISIT), Seoul, South Korea, pp. 729-733, June 2009.

DOI: 10.1109/ISIT.2009.5205679

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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.


MIMO wireless, data detection, sphere-decoding, maximum-likelihood, complexity, random lattices

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