Overview
- Covers the fundamentals of lattices, employing a strongly geometrical and visual approach and accompanying exercises
- Assumes only a minimum of background knowledge on the part of the reader
- Includes applications like the construction of spherical codes using lattices and how to obtain lattices using field theory
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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About this book
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.
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Table of contents (6 chapters)
Authors and Affiliations
About the authors
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.
Frederique Oggier received a PhD in mathematics from the Swiss Federal Institute of Technology (EPFL, before continuing post-doctoral studies at the California Institute of Technology - Caltech, USA,and the Research Center for Information Security at the National Institute of Advanced Industrial and Science Technology, Japan. She is currently an associate professor at Nanyang Technological University, Singapore. Antonio Campelloreceived the PhD degree in Applied Mathematics from the University of Campinas, Brazil, in 2014. He was a visiting academic at the Complutense University of Madrid in 2009, at the École Polytechnique Fédérale de Lausanne (EPFL) in 2011, and at AT&T Research Labs - Shannon Labs, New Jersey in 2013. After spending one year at Télécom Paristech, France, he is currently conducting postdoctoral research at Imperial College London, UK. His research interests are in coding theory, discrete geometry, and communications. Jean-Claude Belfiore received his Engineering degree from the ÉcoleSupérieure d'Electricité - Supelec in 1985, his PhD from Télécom ParisTech in 1989 and his Habilitation from Université Pierre et Marie Curie in 2001. In 1989 he joined the Télécom ParisTech, where he is currently serving as a full professor. He has made pioneering contributions on modulation and coding for wireless systems using tools from number theory. He is also, together with Ghaya Rekaya and Emanuele Viterbo, one of the co-inventors of the celebrated Golden Code. In 2007, he was the recipient of the Blondel Medal. Emanuele Viterbo received his degree in Electrical Engineering in 1989 and his PhD in 1995, also in Electrical Engineering, from the Politecnico di Torino, Italy. He is currently a professor at the Monash University, Australia. His main research interests are in lattice codes for the Gaussian and fading channels, algebraic coding theory, algebraic space-time coding, digital terrestrial television broadcasting, digital magnetic recording, and coding for non-volatile memories.Bibliographic Information
Book Title: Lattices Applied to Coding for Reliable and Secure Communications
Authors: Sueli I.R. Costa, Frédérique Oggier, Antonio Campello, Jean-Claude Belfiore, Emanuele Viterbo
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-67882-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2017
Softcover ISBN: 978-3-319-67881-8Published: 10 April 2018
eBook ISBN: 978-3-319-67882-5Published: 02 April 2018
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: VI, 120
Number of Illustrations: 10 b/w illustrations, 33 illustrations in colour
Topics: Convex and Discrete Geometry, Coding and Information Theory, Cryptology