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Maximum-likelihood decoding and integer least-squares: the expected complexity

Hassibi, Babak and Vikalo, Haris (2003) Maximum-likelihood decoding and integer least-squares: the expected complexity. In: Multiantenna channels : capacity coding and signal processing : DIMACS Workshop Signal Processing for Wireless Transmission, October 7-9, 2002, DIMACS Center. American Mathematical Society , Providence, RI. ISBN 0-8218-3407-X. (Unpublished)

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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 and dimensions, the expected complexity is polynomial, in fact often roughly 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 real-time—a result with many practical implications.

Item Type:Book Section
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Additional Information:© 2003 American Mathematical Society.
Subject Keywords:Integer least-squares problem, sphere decoding, wireless communications, multiple-antenna systems, lattice problems, NP hard, expected complexity, polynomial-time complexity
Record Number:CaltechAUTHORS:20150225-074538196
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55179
Deposited By: Shirley Slattery
Deposited On:05 Mar 2015 19:18
Last Modified:03 Oct 2019 08:03

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