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Sphere packings, lattices, and groups
TLDR
The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?Abstract:
The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics.read more
Citations
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Achieving near-capacity on a multiple-antenna channel
TL;DR: This work provides a simple method to iteratively detect and decode any linear space-time mapping combined with any channel code that can be decoded using so-called "soft" inputs and outputs and shows that excellent performance at very high data rates can be attained with either.
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Unsupervised learning of finite mixture models
TL;DR: The novelty of the approach is that it does not use a model selection criterion to choose one among a set of preestimated candidate models; instead, it seamlessly integrate estimation and model selection in a single algorithm.
Book
Digital Watermarking and Steganography
TL;DR: This new edition now contains essential information on steganalysis and steganography, and digital watermark embedding is given a complete update with new processes and applications.
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A universal lattice code decoder for fading channels
TL;DR: By judicious choice of the decoding radius, it is shown that this maximum-likelihood decoding algorithm can be practically used to decode lattice codes of dimension up to 32 in a fading environment.
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Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions
Alexandr Andoni,Piotr Indyk +1 more
TL;DR: An algorithm for the c-approximate nearest neighbor problem in a d-dimensional Euclidean space, achieving query time of O(dn 1c2/+o(1)) and space O(DN + n1+1c2 + o(1) + 1/c2), which almost matches the lower bound for hashing-based algorithm recently obtained.
References
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Winning ways (for your mathematical plays), vols 1 and 2, by Elwyn R. Berlekamp, John H. Conway and Richard K. Guy. Pp 469 and 475. £10·80 each. 1982. ISBN 0-12-091101-9/02-7 (Academic Press)
Journal ArticleDOI
New bounds on the number of unit spheres that can touch a unit sphere in n dimensions
Andrew Odlyzko,Neil J. A. Sloane +1 more
TL;DR: New upper bounds are given for the maximum number, τ n, of nonoverlapping unit spheres that can touch a unit sphere in n -dimensional Euclidean space, for n ⩽24.
Book
From error-correcting codes through sphere packings to simple groups
TL;DR: From sphere packing to new simple groups is there an interesting group in Leech's lattice?
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The automorphism group of the 26-dimensional even unimodular Lorentzian lattice
TL;DR: The group mentioned in the title is shown to be a certain infinitely generated Coxeter group extended by the negative of the identity operation and the group of all automorphisms of the notorious Leech lattice as discussed by the authors.