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Relevant bibliographies by topics / Lattice Reduction Algorithms

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Academic literature on the topic 'Lattice Reduction Algorithms'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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Journal articles on the topic "Lattice Reduction Algorithms"

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Xu, Hong Sheng, and Ting Zhong Wang. "The Research of Constructing Rough Concept Lattices Model." Applied Mechanics and Materials 63-64 (June 2011): 664–67. http://dx.doi.org/10.4028/www.scientific.net/amm.63-64.664.

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Formal concept lattices and rough set theory are two kinds of complementary mathematical tools for data analysis and data processing. The algorithm of concept lattice reduction based on variable precision rough set is proposed by combining the algorithms of β-upper and lower distribution reduction in variable precision rough set. The traditional algorithms aboutβvalue select algorithm, attribute reduction based on discernibility matrix and extraction rule in VPRS are discussed, there are defects in these traditional algorithms which are improved. Finally, the generation system of concept latti

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Bai, Shi, Thijs Laarhoven, and Damien Stehlé. "Tuple lattice sieving." LMS Journal of Computation and Mathematics 19, A (2016): 146–62. http://dx.doi.org/10.1112/s1461157016000292.

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Lattice sieving is asymptotically the fastest approach for solving the shortest vector problem (SVP) on Euclidean lattices. All known sieving algorithms for solving the SVP require space which (heuristically) grows as $2^{0.2075n+o(n)}$, where $n$ is the lattice dimension. In high dimensions, the memory requirement becomes a limiting factor for running these algorithms, making them uncompetitive with enumeration algorithms, despite their superior asymptotic time complexity.We generalize sieving algorithms to solve SVP with less memory. We consider reductions of tuples of vectors rather than pa

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Guenach, M. "Novel Lattice Reduction Algorithms: Precoder Reduction and Vector Perturbation Tradeoffs." IEEE Communications Letters 22, no. 8 (2018): 1628–31. http://dx.doi.org/10.1109/lcomm.2018.2840994.

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Andrews, Lawrence C., Herbert J. Bernstein, and Nicholas K. Sauter. "A space for lattice representation and clustering." Acta Crystallographica Section A Foundations and Advances 75, no. 3 (2019): 593–99. http://dx.doi.org/10.1107/s2053273319002729.

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Algorithms for quantifying the differences between two lattices are used for Bravais lattice determination, database lookup for unit cells to select candidates for molecular replacement, and recently for clustering to group together images from serial crystallography. It is particularly desirable for the differences between lattices to be computed as a perturbation-stable metric, i.e. as distances that satisfy the triangle inequality, so that standard tree-based nearest-neighbor algorithms can be used, and for which small changes in the lattices involved produce small changes in the distances

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Wen Zhang, Sanzheng Qiao, and Yimin Wei. "HKZ and Minkowski Reduction Algorithms for Lattice-Reduction-Aided MIMO Detection." IEEE Transactions on Signal Processing 60, no. 11 (2012): 5963–76. http://dx.doi.org/10.1109/tsp.2012.2210708.

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Zhou, Qi, and Xiaoli Ma. "Element-Based Lattice Reduction Algorithms for Large MIMO Detection." IEEE Journal on Selected Areas in Communications 31, no. 2 (2013): 274–86. http://dx.doi.org/10.1109/jsac.2013.130215.

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Zhou, Qi, and Xiaoli Ma. "Improved Element-Based Lattice Reduction Algorithms for Wireless Communications." IEEE Transactions on Wireless Communications 12, no. 9 (2013): 4414–21. http://dx.doi.org/10.1109/twc.2013.072513.121479.

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Schnorr, C. P. "A hierarchy of polynomial time lattice basis reduction algorithms." Theoretical Computer Science 53, no. 2-3 (1987): 201–24. http://dx.doi.org/10.1016/0304-3975(87)90064-8.

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Wang, Li-Ping. "Lattice basis reduction algorithms and multi-dimensional continued fractions." Finite Fields and Their Applications 14, no. 4 (2008): 979–91. http://dx.doi.org/10.1016/j.ffa.2008.05.008.

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de Weger, B. M. M. "Solving exponential diophantine equations using lattice Basis Reduction Algorithms." Journal of Number Theory 26, no. 3 (1987): 325–67. http://dx.doi.org/10.1016/0022-314x(87)90088-6.

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Dissertations / Theses on the topic "Lattice Reduction Algorithms"

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Weldu, Hailay Gidey. "Analysis of Lattice Reduction Algorithms : Solving SVP Challenges." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-75552.

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Lattice-based cryptography which holds a great promise for post-quantum cryptographyis naturally concerned by lattice reduction algorithms, the essential tools in the algorithmicstudy of lattices and its applications. In order to precisely estimate the securityparameters of these cryptosystems, it is a necessity to assess the practical diculty of theshortest vector problem (SVP) by analyzing the known ecient algorithms for solvingit.In this thesis project, we revisit a recursive lattice reduction methodology going back toPlantard & Susilo's work (SCN 2010) and analyze practicality of an SV

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Gestner, Brian Joseph. "Lattice reduction for MIMO detection: from theoretical analysis to hardware realization." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39591.

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The objective of the dissertation research is to understand the complex interaction between the algorithm and hardware aspects of symbol detection that is enhanced by lattice reduction (LR) preprocessing for wireless MIMO communication systems. The motivation for this work stems from the need to improve the bit-error-rate performance of conventional, low-complexity detectors while simultaneously exhibiting considerably reduced complexity when compared to the optimal method, maximum likelihood detection. Specifically, we first develop an understanding of the complex Lenstra-Lenstra-Lovász (CLLL

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Cimen, Canan. "On The Ntru Public Key Cryptosystem." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/3/12609848/index.pdf.

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NTRU is a public key cryptosystem, which was first introduced in 1996. It is a ring-based cryptosystem and its security relies on the complexity of a well-known lattice problem, i.e. shortest vector problem (SVP). There is no efficient algorithm known to solve SVP exactly in arbitrary high dimensional lattices. However, approximate solutions to SVP can be found by lattice reduction algorithms. LLL is the first polynomial time algorithm that finds reasonable short vectors of a lattice. The best known attacks on the NTRU cryptosystem are lattice attacks. In these attacks, the lattice construct

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Roger, Varea Sandra. "Design and Implementation of Efficient Algorithms for Wireless MIMO Communication Systems." Doctoral thesis, Universitat Politècnica de València, 2012. http://hdl.handle.net/10251/16562.

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En la última década, uno de los avances tecnológicos más importantes que han hecho culminar la nueva generación de banda ancha inalámbrica es la comunicación mediante sistemas de múltiples entradas y múltiples salidas (MIMO). Las tecnologías MIMO han sido adoptadas por muchos estándares inalámbricos tales como LTE, WiMAS y WLAN. Esto se debe principalmente a su capacidad de aumentar la máxima velocidad de transmisión , junto con la fiabilidad alcanzada y la cobertura de las comunicaciones inalámbricas actuales sin la necesidad de ancho de banda extra ni de potencia de transmisión adicional. Si

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Waters, Deric Wayne. "Signal Detection Strategies and Algorithms for Multiple-Input Multiple-Output Channels." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7514.

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In todays society, a growing number of users are demanding more sophisticated services from wireless communication devices. In order to meet these rising demands, it has been proposed to increase the capacity of the wireless channel by using more than one antenna at the transmitter and receiver, thereby creating multiple-input multiple-output (MIMO) channels. Using MIMO communication techniques is a promising way to improve wireless communication technology because in a rich-scattering environment the capacity increases linearly with the number of antennas. However, increasing the number of tr

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Zhang, Yuqi. "Lattice Reduction Aided Multiple Input Multiple Output Detection Algorithm Design For 5G Communication." Thesis, KTH, Teknisk informationsvetenskap, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-209559.

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In recent years, multiple input multiple output system has raised intensive researchinterests for its huge potentials to achieve higher spectral efficiency anddata rate. However, transmitting multiple data streams through the same timeand frequency resources simultaneously leads to severe interference betweentransmitted signals. In order to solve this problem, lattice reduction is proposedas a suboptimal maximum likelihood algorithm. It aims at finding aset of better basis vectors for the channel matrix and results in satisfactoryperformance improvements compared to conventional linear detecto

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Kapfunde, Goodwell. "Near-capacity sphere decoder based detection schemes for MIMO wireless communication systems." Thesis, University of Hertfordshire, 2013. http://hdl.handle.net/2299/11350.

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The search for the closest lattice point arises in many communication problems, and is known to be NP-hard. The Maximum Likelihood (ML) Detector is the optimal detector which yields an optimal solution to this problem, but at the expense of high computational complexity. Existing near-optimal methods used to solve the problem are based on the Sphere Decoder (SD), which searches for lattice points confined in a hyper-sphere around the received point. The SD has emerged as a powerful means of finding the solution to the ML detection problem for MIMO systems. However the bottleneck lies in the de

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LaMacchia, Brian A. "Basis Reduction Algorithms and Subset Sum Problems." 1991. http://hdl.handle.net/1721.1/6813.

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This thesis investigates a new approach to lattice basis reduction suggested by M. Seysen. Seysen's algorithm attempts to globally reduce a lattice basis, whereas the Lenstra, Lenstra, Lovasz (LLL) family of reduction algorithms concentrates on local reductions. We show that Seysen's algorithm is well suited for reducing certain classes of lattice bases, and often requires much less time in practice than the LLL algorithm. We also demonstrate how Seysen's algorithm for basis reduction may be applied to subset sum problems. Seysen's technique, used in combination with the LLL algor

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Wang, Chih-Chng, and 王致忠. "A Low-Complexity Lattice-Reduction aided MIMO Detection Using Random and Tree-Search Algorithms." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/66811095663842336772.

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碩士<br>國立臺北大學<br>通訊工程研究所<br>103<br>The MIMO detector plays a very important role in the communication structure. Detection methods will directly affect the quality of communication. In this paper we compare the difference between tree-search algorithm and random rounding-off algorithm, and combine their advantages into hybrid search. In this process, we add the Lattice-Reduction to help us to get better communication quality. Finally, we will present the results in the last chapter.

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Shabany, Mahdi. "VLSI Implementation of Digital Signal Processing Algorithms for MIMO/SISO Systems." Thesis, 2009. http://hdl.handle.net/1807/17485.

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The efficient high-throughput VLSI implementation of near-optimal multiple-input multiple-output (MIMO) detectors for 4x4 MIMO systems in high-order quadrature amplitude modulation (QAM) schemes has been a major challenge in the literature. To address this challenge, this thesis introduces a novel scalable pipelined VLSI architecture for a 4x4 64-QAM MIMO receiver based on K-Best lattice decoders. The key contribution is a means of expanding/visiting the intermediate nodes of the search tree on-demand, rather than exhaustively along with three types of distributed sorters operating in a pipel

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Books on the topic "Lattice Reduction Algorithms"

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Lattice basis reduction: An introduction to the LLL algorithm and its applications. Taylor & Francis, 2012.

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Bremner, Murray R. Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications. Taylor & Francis Group, 2011.

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Book chapters on the topic "Lattice Reduction Algorithms"

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Vallée, Brigitte, and Antonio Vera. "Probabilistic Analyses of Lattice Reduction Algorithms." In The LLL Algorithm. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02295-1_3.

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Nguyen, Phong Q. "Lattice Reduction Algorithms: Theory and Practice." In Advances in Cryptology – EUROCRYPT 2011. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20465-4_2.

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Ludwig, Christoph. "A Faster Lattice Reduction Method Using Quantum Search." In Algorithms and Computation. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-24587-2_22.

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Schnorr, C. P., and M. Euchner. "Lattice basis reduction: Improved practical algorithms and solving subset sum problems." In Fundamentals of Computation Theory. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-54458-5_51.

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Backes, Werner, and Susanne Wetzel. "Lattice Basis Reduction with Dynamic Approximation." In Algorithm Engineering. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44691-5_6.

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Schnorr, Claus Peter. "Progress on LLL and Lattice Reduction." In The LLL Algorithm. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02295-1_4.

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Semaev, Igor. "A 3-Dimensional Lattice Reduction Algorithm." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44670-2_13.

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Akhavi, Ali. "Threshold Phenomena in Random Lattices and Efficient Reduction Algorithms." In Algorithms - ESA’ 99. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-48481-7_41.

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Schnorr, C. P. "A more efficient algorithm for lattice basis reduction." In Automata, Languages and Programming. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/3-540-16761-7_85.

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Cucinotta, Filippo, Marcello Raffaele, and Fabio Salmeri. "A Topology Optimization Method for Stochastic Lattice Structures." In Lecture Notes in Mechanical Engineering. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-70566-4_38.

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AbstractStochastic lattice structures are very powerful solutions for filling three-dimensional spaces using a generative algorithm. They are suitable for 3D printing and are well appropriate to structural optimization and mass distribution, allowing for high-performance and low-weight structures. The paper shows a method, developed in the Rhino-Grasshopper environment, to distribute lattice structures until a goal is achieved, e.g. the reduction of the weight, the harmonization of the stresses or the limitation of the strain. As case study, a cantilever beam made of Titan alloy, by means of SLS technology has been optimized. The results of the work show the potentiality of the methodology, with a very performing structure and low computational efforts.

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Conference papers on the topic "Lattice Reduction Algorithms"

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Stehlé, Damien. "Lattice Reduction Algorithms." In ISSAC '17: International Symposium on Symbolic and Algebraic Computation. ACM, 2017. http://dx.doi.org/10.1145/3087604.3087665.

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Zhou, ShiXiang, Chao Yin, and Hui Xu. "Research Progress of Lattice Bases Reduction Algorithms." In 2012 International Conference on Computer Science and Electronics Engineering (ICCSEE). IEEE, 2012. http://dx.doi.org/10.1109/iccsee.2012.366.

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Zhou, Qi, and Xiaoli Ma. "Joint transceiver designs using lattice reduction algorithms." In 2013 IEEE China Summit and International Conference on Signal and Information Processing (ChinaSIP). IEEE, 2013. http://dx.doi.org/10.1109/chinasip.2013.6625408.

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Ying Hung Gan and Wai How Mow. "Complex lattice reduction algorithms for low-complexity MIMO detection." In GLOBECOM '05. IEEE Global Telecommunications Conference, 2005. IEEE, 2005. http://dx.doi.org/10.1109/glocom.2005.1578299.

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Haque, Md Mokammel, and Josef Pieprzyk. "Evaluating the performance of the practical lattice reduction algorithms." In 2014 8th International Conference on Electrical and Computer Engineering (ICECE). IEEE, 2014. http://dx.doi.org/10.1109/icece.2014.7026884.

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Barbero, Luis G., T. Ratnarajah, and Colin Cowan. "A Comparison of Complex Lattice Reduction Algorithms for MIMO Detection." In ICASSP 2008. IEEE International Conference on Acoustic, Speech and Signal Processes. IEEE, 2008. http://dx.doi.org/10.1109/icassp.2008.4518207.

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Lu, Xiaojia, Pirkka Silvola, and Markku Juntti. "Lattice Reduction Based Detection Algorithms in High Correlated MIMO-OFDM System." In 2006 IEEE 17th International Symposium on Personal, Indoor and Mobile Radio Communications. IEEE, 2006. http://dx.doi.org/10.1109/pimrc.2006.254001.

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Gestner, Brian, and David V. Anderson. "Single newton-raphson iteration for integer-rounded divider for lattice reduction algorithms." In 2008 51st IEEE International Midwest Symposium on Circuits and Systems (MWSCAS). IEEE, 2008. http://dx.doi.org/10.1109/mwscas.2008.4616962.

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Youssef, Ameer, Mahdi Shabany, and P. Glenn Gulak. "Performance analysis of lattice-reduction algorithms for a novel LR-compatible K-Best MIMO detector." In 2011 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2011. http://dx.doi.org/10.1109/iscas.2011.5937662.

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Das, Dipayan, and Vishal Saraswat. "A Novel Lattice Reduction Algorithm." In International Conference on Security and Cryptography. SCITEPRESS - Science and Technology Publications, 2018. http://dx.doi.org/10.5220/0006862104960501.

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