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Fast Lattice Point Enumeration with Minimal Overhead [chapter]

Daniele Micciancio, Michael Walter
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
However, there is an uncomfortable gap between our theoretical understanding and practical performance of lattice point enumeration algorithms.  ...  technique that can be directly applied to projected lattice (basis) vectors, without the need to remove linear dependencies, and a modified block basis reduction method with fast (logarithmic) convergence  ...  time and minimal overhead.  ... 
doi:10.1137/1.9781611973730.21 dblp:conf/soda/MicciancioW15 fatcat:wf3jvwa47falzk4nuabsayq2yi

Lattice Reduction Aided Selective Spanning With Fast Enumeration For Soft-Output Mimo Detection

Ubaid Ahmad, Claude Desset, Rudy Lauwereins, Min Li, Sofie Pollin, Liesbet Van der Perre
2012 Zenodo  
Fast Enumeration ins − domain In FE the first point is always set to p 1 =s LRZF (m i = 1) to guarantee the ML diversity. The closest constellation point tos LRZF + e α is p 2 = Q(s LRZF + e α ).  ...  In order to achieve near-MAP performance with LR-aided soft output MIMO detection on a parallel programmable architecture, we propose LR-aided SSFE (Selective Spanning with Fast Enumeration).  ... 
doi:10.5281/zenodo.52328 fatcat:b5ffmw7iqzf4tpshlxohijqebm

Fast and Area-Efficient Sphere Decoding Using Look-Ahead Search

Se-Hyeon Kang, In-Cheol Park
2007 2007 IEEE 65th Vehicular Technology Conference - VTC2007-Spring  
This paper proposes a fast decoding algorithm to reduce the decoding cycles using look-ahead search.  ...  Scaling and enumeration techniques are also presented, which are effective in implementing the proposed sphere decoder.  ...  PROPOSED SPHERE DECODER This section describes a fast decoding algorithm to save redundant decoding cycles with small hardware overhead.  ... 
doi:10.1109/vetecs.2007.492 dblp:conf/vtc/KangP07 fatcat:lvts2uy6bfberbtuxdvgrkkyey

24-Dimensional Modulation Formats for 100 Gbit/s IM-DD Transmission Systems Using 850 nm Single-Mode VCSEL

Xiaofeng Lu, Vladimir S. Lyubopytov, Idelfonso Tafur Monroy
2017 2017 European Conference on Optical Communication (ECOC)  
Acknowledgements This work is partly financed by the HOT project of the Danish Innovation Fund in association with Mellanox Technologies. The authors also thank Keysight for providing AWG.  ...  And then the enumeration requires only the summations of the G 24 code words. The fast decoding of the Golay code and the Leech lattice modulation have been well discussed 9 .  ...  FEC schemes with minimized latency is crucial.  ... 
doi:10.1109/ecoc.2017.8345840 fatcat:nhowogx25zeyjpxxy3s2voorni

A New Angle on Lattice Sieving for the Number Field Sieve [article]

Gary McGuire, Oisin Robinson
2020 arXiv   pre-print
We use the successive minima and shortest vectors of the lattice instead of transition vectors to iterate through lattice points.  ...  The main contribution of this article is to show that a different method of lattice enumeration in three dimensions will provide a significant speedup.  ...  Our approach is very simple: to enumerate all lattice points in H, we enumerate all points in the ground plane G that lie in H, and then all points in the translates G + kv 3 for k = 1, 2, 3, ... that  ... 
arXiv:2001.10860v1 fatcat:26v5byjcircv5pc4n3woei4kni

Tile size selection for optimized memory reuse in high-level synthesis

Junyi Liu, John Wickerson, George A. Constantinides
2017 2017 27th International Conference on Field Programmable Logic and Applications (FPL)  
To determine the tile size for data reuse in constrained on-chip memory, an algorithm is then developed to optimize over this model, using non-linear solvers to minimize communication overhead.  ...  communication overhead.  ...  In geometric terms, this lattice should have no intersection with the polytope of K b except the zero point.  ... 
doi:10.23919/fpl.2017.8056810 dblp:conf/fpl/LiuWC17 fatcat:34vhbzckrbc6lkrzg7tjhhiqqe

Scalable algorithms for association mining

M.J. Zaki
2000 IEEE Transactions on Knowledge and Data Engineering  
The algorithms utilize the structural properties of frequent itemsets to facilitate fast discovery.  ...  We also present the effect of using different database layout schemes combined with the proposed decomposition and traversal techniques.  ...  Another way to minimize the I/O overhead is to work with only a small sample of the database.  ... 
doi:10.1109/69.846291 fatcat:cnmc63m4zvfdjbcfde7lmulory

Lattice Sieving in Three Dimensions for Discrete Log in Medium Characteristic

Gary McGuire, Oisín Robinson
2020 Journal of Mathematical Cryptology  
Our method is to use the successive minima and shortest vectors of the lattice instead of transition vectors to iterate through lattice points.  ...  We showcase the new method by a record computation in a 133-bit subgroup of ${{\mathbb{F}}_{{{p}^{6}}}}$, with p6 having 423 bits.  ...  The less dense lattices (not for small primes) should be sieved, and our lattice enumeration method will be very fast here. Remark 10.  ... 
doi:10.1515/jmc-2020-0008 fatcat:t5rj4mip6za4xiztfjrjmfenjm

Algorithm 958

Pierre L'ecuyer, David Munger
2016 ACM Transactions on Mathematical Software  
For numbers of points that are integer powers of a prime base, the construction of embedded rank-1 lattice rules is supported through any of the above algorithms, and also through a fast CBC algorithm,  ...  It supports exhaustive and random searches, as well as component-by-component (CBC) and random CBC constructions, for any number of points, and for various measures of (non)uniformity of the points.  ...  a 1 , . . . , a s , selected to minimize the figure of merit of the resulting extended n m+1 -point lattice.  ... 
doi:10.1145/2754929 fatcat:fk2ewft2anczzbylz2t7nsuhxi

Designing Voronoi Constellations to Minimize Bit Error Rate

Shen Li, Ali Mirani, Magnus Karlsson, Erik Agrell
2021 2021 IEEE International Symposium on Information Theory (ISIT)  
To minimize the bit error rate (BER), pseudo-Gray labeling of constellation points is applied.  ...  In this work, we design VCs with a cubic coding lattice based on Kurkoski's encoding and decoding algorithms.  ...  This enumeration admits very fast encoding and decoding algorithms, which are reviewed by Zamir in [16, Ch. 9], [17] .  ... 
doi:10.1109/isit45174.2021.9517815 fatcat:z3hpffmwjvcf7gvbmtv3awjnqe

Quantum Lattice Enumeration and Tweaking Discrete Pruning [chapter]

Yoshinori Aono, Phong Q. Nguyen, Yixin Shen
2018 Lecture Notes in Computer Science  
Enumeration is a fundamental lattice algorithm.  ...  We show how to speed up enumeration on a quantum computer, which affects the security estimates of several lattice-based submissions to NIST: if T is the number of operations of enumeration, our quantum  ...  And if one enumerates π k+1 (L) ∩ S for some k ≥ 1, one can derive π k (L) ∩ S by enumerating the intersection of a one-dimensional lattice with a suitable ball, for each point in π k+1 (L) ∩ S.  ... 
doi:10.1007/978-3-030-03326-2_14 fatcat:ol3gxm6lc5bpxlqpijtxnx4dfq

Rigorous and Efficient Short Lattice Vectors Enumeration [chapter]

Xavier Pujol, Damien Stehlé
2008 Lecture Notes in Computer Science  
In the context of the fast developing lattice-based cryptography, the practical security estimates derive from floating-point implementations of these algorithms.  ...  The Kannan-Fincke-Pohst enumeration algorithm for the shortest and closest lattice vector problems is the keystone of all strong lattice reduction algorithms and their implementations.  ...  The following theorem shows that the overhead of the floating-point enumeration with respect to the rational one is small.  ... 
doi:10.1007/978-3-540-89255-7_24 fatcat:bbgpqtzwhjbw3blroi24hyy74m

Scalable discovery of unique column combinations

Arvid Heise, Jorge-Arnulfo Quiané-Ruiz, Ziawasch Abedjan, Anja Jentzsch, Felix Naumann
2013 Proceedings of the VLDB Endowment  
To achieve even higher scalability, Ducc runs on several CPU cores (scale-up) and compute nodes (scale-out) with a very low overhead.  ...  We exhaustively evaluate Ducc using three datasets (two real and one synthetic) with several millions rows and hundreds of attributes. We compare Ducc with related work: Gordian and HCA.  ...  At the same time, the worker enumerates all pairs of non-unique columns as seeds, i.e., as starting points for the graph traversal (Line 3).  ... 
doi:10.14778/2732240.2732248 fatcat:dtty4gpsovh57em2mitrfwltla

Multiple-antenna differential lattice decoding

Cong Ling, Wai Ho Mow, K.H. Li, A.C. Kot
2005 IEEE Journal on Selected Areas in Communications  
We first analyze two distinct approximate DLD algorithms, and then develop an algorithm that exactly finds the closest lattice point in the Euclidean space.  ...  Their approximate decoding algorithm, however, has not unleashed the full potential of lattice decoding.  ...  The Schnorr-Euchner strategy can also be modified to enumerate all lattice points inside a sphere for one with the maximum MLD metric.  ... 
doi:10.1109/jsac.2005.853795 fatcat:vi5xeh5kgjgi5csuo333tth5sa

The design of efficient algorithms for enumeration [article]

Andrew R. Conway
2017 arXiv   pre-print
Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects.  ...  For those new to the field, this paper is designed to be an introduction to many of the tricks for producing efficient enumeration algorithms.  ...  Enumerating on the n by m lattice is usually the same as the m by n lattice. The orientation is chosen to minimize the length of the boundary, and thus the number of states.  ... 
arXiv:1610.09806v2 fatcat:bfk2mrmekvbkfhk5l5coyz2gxm
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