NDLI: On the expected complexity of integer least-squares problems

Content Provider	IEEE Xplore Digital Library
Author	Hassibi, Babak Vikalo, Haris
Copyright Year	2002
Description	Author affiliation: Department of Electrical Engineering, California Institute of Technology, Pasadena, 91125, USA (Hassibi, Babak) \|\| Information Systems Laboratory, Stanford University, CA 94305, USA (Vikalo, Haris)
Abstract	The problem of finding the least-squares solution to a system of linear equations where the unknown vector is comprised of integers, but the matrix coefficient and given vector are comprised of real numbers, arises in many applications: communications, cryptography, GPS, to name a few. The problem is equivalent to finding the closest lattice point to a given point and is known to be NP-hard. In communications applications, however, the given vector is not arbitrary, but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known. Therefore in this paper, rather than dwell on the worst-case complexity of the integer-least-squares problem, we study its expected complexity, averaged over the noise and over the lattice. For the “sphere decoding” algorithm of Fincke and Pohst we find a closed-form expression for the expected complexity and show that for a wide range of noise variances the expected complexity is polynomial, in fact often sub-cubic. Since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial, this suggests that maximum-likelihood decoding, which was hitherto thought to be computationally intractable, can in fact be implemented in realtime—a result with many practical implications.
File Size	829173
File Format	PDF
ISBN	0780374029
ISSN	15206149
DOI	10.1109/ICASSP.2002.5744897
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2002-05-13
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Artificial neural networks Cryptography Ear Artificial intelligence Computational modeling Decoding Antennas
Content Type	Text
Resource Type	Article

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