Lattices Applied to Coding for Reliable and Secure Communications

Sueli I.R. Costa, Frédérique Oggier, Antonio Campello, Jean-Claude Belfiore, Emanuele Viterbo (Autoren)

Buch | Softcover

VI, 120 Seiten

2018 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-67881-8 (ISBN)

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This book provides a first course on lattices - mathematical objects pertaining to the realm of discrete geometry, which are of interest to mathematicians for their structure and, at the same time, are used by electrical and computer engineers working on coding theory and cryptography. The book presents both fundamental concepts and a wealth of applications, including coding and transmission over Gaussian channels, techniques for obtaining lattices from finite prime fields and quadratic fields, constructions of spherical codes, and hard lattice problems used in cryptography. The topics selected are covered in a level of detail not usually found in reference books. As the range of applications of lattices continues to grow, this work will appeal to mathematicians, electrical and computer engineers, and graduate or advanced undergraduate in these fields.

Sueli I. R. Costa received her PhD in Mathematics from the University of Campinas, Brazil, and pursued her post-doctoral studies at the Institute for Advanced Study - IAS, Princeton, USA. She is a professor at the Institute of Mathematics of University of Campinas and her recent research activities in lattice coding and information include short-term visits to the Bernoulli Centre, EPFL, Switzerland; the AT&T Research Lab, USA, Télécom ParisTech, France, and serving as chair of the IEEE-Information Theory Society Brazil Chapter.

Introduction.- Lattices and Applications.- Lattices from Codes.- Ideal Lattices.- Lattices and Spherical Codes.- Lattice and Index Coding.

Erscheinungsdatum	22.03.2018
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	VI, 120 p. 43 illus., 33 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	191 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebraic Geometry • Coding and information theory • coding theory • Coding theory & cryptology • Coding theory & cryptology • convex and discrete Geometry • cryptography • data encryption • Discrete Mathematics • Gaussian Channel • index coding • Information Theory • lattices • Mathematics • mathematics and statistics • signal transmission • spherical codes
ISBN-10	3-319-67881-7 / 3319678817
ISBN-13	978-3-319-67881-8 / 9783319678818
Zustand	Neuware