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Lattices that admit logarithmic worstcase to averagecase connection factors
, 2006
"... We demonstrate an averagecase problem which is as hard as finding γ(n)approximate shortest vectors in certain ndimensional lattices in the worst case, where γ(n) = O( log n). The previously best known factor for any class of lattices was γ(n) = Õ(n). To obtain our results, we focus on families ..."
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Cited by 23 (11 self)
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We demonstrate an averagecase problem which is as hard as finding γ(n)approximate shortest vectors in certain ndimensional lattices in the worst case, where γ(n) = O( log n). The previously best known factor for any class of lattices was γ(n) = Õ(n). To obtain our results, we focus
Blind Beamforming for Non Gaussian Signals
 IEE ProceedingsF
, 1993
"... This paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resorting to their hypothesized value. By using estimates of the directional vectors obtained via blind identification i.e. without knowing the arrray mani ..."
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Cited by 704 (31 self)
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estimation of directional vectors, based on joint diagonalization of 4thorder cumulant matrices
Image denoising using a scale mixture of Gaussians in the wavelet domain
 IEEE TRANS IMAGE PROCESSING
, 2003
"... We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vecto ..."
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Cited by 514 (17 self)
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We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian
WorstCase Vs. Algorithmic AverageCase Complexity in the PolynomialTime Hierarchy
 In Proceedings of the 10th International Workshop on Randomization and Computation, RANDOM 2006
, 2006
"... We show that for every integer k> 1, if Σk, the k’th level of the polynomialtime hierarchy, is worstcase hard for probabilistic polynomialtime algorithms, then there is a language L ∈ Σk such that for every probabilistic polynomialtime algorithm that attempts to decide it, there is a samplabl ..."
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Cited by 2 (1 self)
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We show that for every integer k> 1, if Σk, the k’th level of the polynomialtime hierarchy, is worstcase hard for probabilistic polynomialtime algorithms, then there is a language L ∈ Σk such that for every probabilistic polynomialtime algorithm that attempts to decide it, there is a
The stretchlength tradeoff in geometric networks: Worstcase and averagecase study
 In preparation
, 2010
"... ar ..."
WORST AND AVERAGECASE COMPLEXITY OF LLL LATTICE REDUCTION IN MIMO WIRELESS SYSTEMS
"... Lattice reduction by means of the LLL algorithm has been previously suggested as a powerful preprocessing tool that allows to improve the performance of suboptimal detectors and to reduce the complexity of optimal MIMO detectors. The complexity of the LLL algorithm is often cited as polynomial in th ..."
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Cited by 2 (0 self)
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in the dimension of the lattice. In this paper we argue that this statement is not correct when made in the MIMO context. Specifically, we demonstrate that in typical communication scenarios the worstcase complexity of the LLL algorithm is not even finite. For i.i.d. Rayleigh fading channels, we further prove
A WorstCase to AverageCase Connection for CVP
"... We prove a connection of the worstcase complexity and the averagecase complexity for the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP for lattices under a certain natural distribution, at least with ..."
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We prove a connection of the worstcase complexity and the averagecase complexity for the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP for lattices under a certain natural distribution, at least
AverageCase Intractability vs. WorstCase Intractability
 IN THE 23RD INTERNATIONAL SYMPOSIUM ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
, 1998
"... We use the assumption that all sets in NP (or other levels of the polynomialtime hierarchy) have efficient averagecase algorithms to derive collapse consequences for MA, AM, and various subclasses of P/poly. As a further consequence we show for C 2 fP(PP);PSPACEg that C is not tractable in the a ..."
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Cited by 3 (1 self)
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We use the assumption that all sets in NP (or other levels of the polynomialtime hierarchy) have efficient averagecase algorithms to derive collapse consequences for MA, AM, and various subclasses of P/poly. As a further consequence we show for C 2 fP(PP);PSPACEg that C is not tractable
WorstCase Running Times for AverageCase Algorithms
"... Abstract—Under a standard hardness assumption we exactly characterize the worstcase running time of languages that are in average polynomialtime over all polynomialtime samplable distributions. More precisely we show that if exponential time is not infinitely often in subexponential space, then t ..."
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Cited by 3 (0 self)
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Abstract—Under a standard hardness assumption we exactly characterize the worstcase running time of languages that are in average polynomialtime over all polynomialtime samplable distributions. More precisely we show that if exponential time is not infinitely often in subexponential space
Results 11  20
of
1,580,777