In practical finite-impulse-response (FIR) digital filter applications, it is often necessary to represent the filter coefficients with a finite number of bits. The finite wordlength restriction increases the filter d...
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In practical finite-impulse-response (FIR) digital filter applications, it is often necessary to represent the filter coefficients with a finite number of bits. The finite wordlength restriction increases the filter deviation. This increase can be reduced substantially if the optimal finite wordlength coefficients are used. The time needed to compute these coefficients is greatly reduced with the help of a lower bound on the deviation increase. Derivation of an improved lower bound that uses the well-known lll algorithm is presented in this correspondence.
The Lenstra-Lenstra-Lovasz (lll) algorithm is a popular lattice reduction algorithm in communications. In this paper, variants of the lll algorithm with either reduced or fixed complexity are proposed and analyzed. Sp...
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The Lenstra-Lenstra-Lovasz (lll) algorithm is a popular lattice reduction algorithm in communications. In this paper, variants of the lll algorithm with either reduced or fixed complexity are proposed and analyzed. Specifically, the use of effective lll reduction for lattice decoding is presented, where size reduction is only performed for pairs of consecutive basis vectors. Its average complexity (measured by the number of floating-point operations and averaged over i.i.d. standard normal lattice bases) is shown to be O(n(3) logn), where n is the lattice dimension. This average complexity is an order lower than previously thought. To address the issue of variable complexity of the lll algorithm, two fixed-complexity approximations are proposed. One is fixed-complexity effective lll, for which the first vector of the basis is proven to be bounded in length;the other is fixed-complexity lll with deep insertion, which is shown to be closely related to the well known V-BLAST algorithm. Such fixed-complexity structures are much desirable in hardware implementation since they allow straightforward constant-throughput implementation.
The lll algorithm has received a lot of attention as an effective numerical tool for preconditioning an integer least squares problem. However, the workings of the algorithm are not well understood. In this paper, we ...
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The lll algorithm has received a lot of attention as an effective numerical tool for preconditioning an integer least squares problem. However, the workings of the algorithm are not well understood. In this paper, we present a new way to look at the lll reduction, which leads to a new implementation method that performs better than the original lll scheme. (c) 2007 Elsevier Inc. All rights reserved.
The study of paper "Cryptanalysis of RSA with Private Key d less than N-0.292, [IEEE Trans. Information Theory, 46 (2000) 1339], which Boneh and Durfee published in IEEE Transactions on Information Theory in July...
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The study of paper "Cryptanalysis of RSA with Private Key d less than N-0.292, [IEEE Trans. Information Theory, 46 (2000) 1339], which Boneh and Durfee published in IEEE Transactions on Information Theory in July 2000, supported that when d < N-0.292, the RSA system can be cracked by using the lll algorithm. In this paper, we find ways to utilize the lll algorithm to break the RSA system even when the value of d is large. According to the proposed cryptanalysis, if d satisfies vertical bar lambda - d vertical bar < N-0.25, the RSA system will be possible to be resolved computationally. (c) 2004 Elsevier Inc. All rights reserved.
A common technique to perform lattice basis reduction is the Lenstra, Lenstra, Lovasz (lll) algorithm. An implementation of this algorithm in real-time systems suffers from the problem of variable run-time and complex...
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A common technique to perform lattice basis reduction is the Lenstra, Lenstra, Lovasz (lll) algorithm. An implementation of this algorithm in real-time systems suffers from the problem of variable run-time and complexity. This correspondence proposes a modification of the lll algorithm. The signal flow is altered to follow a deterministic structure, which promises to obtain an easier implementation as well as a fixed execution time known in advance. In the case of a maximum number of iterations as it is likely in real-time systems, our modification clearly outperforms the original lll algorithm as far as the quality of the reduced lattice basis is concerned.
Luk and Tracy (2008) [7] developed a matrix interpretation of the lll algorithm. Building on their work [7], we propose to add pivoting to the algorithm. We prove that our new algorithm always terminates, and we const...
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Luk and Tracy (2008) [7] developed a matrix interpretation of the lll algorithm. Building on their work [7], we propose to add pivoting to the algorithm. We prove that our new algorithm always terminates, and we construct a class of ill-conditioned reduced matrices to illustrate the advantages of pivoting. (C) 2010 Elsevier Inc. All rights reserved.
The lll algorithm is widely used to solve the integer least squares problems that arise in many engieering applications. As most practitioners did not understand how the lll algorithm works, they avoided the issue by ...
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ISBN:
(纸本)9780819468451
The lll algorithm is widely used to solve the integer least squares problems that arise in many engieering applications. As most practitioners did not understand how the lll algorithm works, they avoided the issue by referring to the method as an integer Gram Schmidt approach (without explaining what they mean by this term). Luk and Tracy(1) were first to describe the behavior of the lll algorithm, and they presented a new numerical implementation that should be more robust than the original lll scheme. In this paper, we compare the numerical properties of the two different lll implementations.
Luk and Tracy (2008) [7] developed a matrix interpretation of the lll algorithm. Building on their work [7], we propose to add pivoting to the algorithm. We prove that our new algorithm always terminates, and we const...
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Luk and Tracy (2008) [7] developed a matrix interpretation of the lll algorithm. Building on their work [7], we propose to add pivoting to the algorithm. We prove that our new algorithm always terminates, and we construct a class of ill-conditioned reduced matrices to illustrate the advantages of pivoting. (C) 2010 Elsevier Inc. All rights reserved.
The lll algorithm is a well-known and widely used lattice basis reduction algorithm. hi many applications, its speed is critical. Parallel computing can improve speed. However, the original lll is sequential in nature...
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ISBN:
(纸本)9781450306263
The lll algorithm is a well-known and widely used lattice basis reduction algorithm. hi many applications, its speed is critical. Parallel computing can improve speed. However, the original lll is sequential in nature. In this paper, we present a multi-threading lll algorithm based on a recently unproved version: all lll algorithm with delayed size reduction.
This paper presents a study of the lll algorithm from the perspective of statistical physics. Based on our experimental and theoretical results, we suggest that interpreting lll as a sandpile model may help understand...
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