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Lattices Applied to Coding for Reliable and Secure Communications

  • Sueli I.R. Costa
  • Frédérique Oggier
  • Antonio Campello
  • Jean-Claude Belfiore
  • Emanuele Viterbo

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Sueli I. R. Costa, Frédérique Oggier, Antonio Campello, Jean-Claude Belfiore, Emanuele Viterbo
    Pages 1-3
  3. Sueli I. R. Costa, Frédérique Oggier, Antonio Campello, Jean-Claude Belfiore, Emanuele Viterbo
    Pages 5-36
  4. Sueli I. R. Costa, Frédérique Oggier, Antonio Campello, Jean-Claude Belfiore, Emanuele Viterbo
    Pages 37-58
  5. Sueli I. R. Costa, Frédérique Oggier, Antonio Campello, Jean-Claude Belfiore, Emanuele Viterbo
    Pages 59-71
  6. Sueli I. R. Costa, Frédérique Oggier, Antonio Campello, Jean-Claude Belfiore, Emanuele Viterbo
    Pages 73-92
  7. Sueli I. R. Costa, Frédérique Oggier, Antonio Campello, Jean-Claude Belfiore, Emanuele Viterbo
    Pages 93-111
  8. Back Matter
    Pages 113-120

About this book

Introduction

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.

Keywords

lattices coding theory signal transmission cryptography Gaussian channel index coding spherical codes

Authors and affiliations

  • Sueli I.R. Costa
    • 1
  • Frédérique Oggier
    • 2
  • Antonio Campello
    • 3
  • Jean-Claude Belfiore
    • 4
  • Emanuele Viterbo
    • 5
  1. 1.Institute of Mathematics, Statistics and Computer ScienceUniversity of CampinasCampinasBrazil
  2. 2.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore
  3. 3.Department of Electrical and Electronic EngineeringImperial College LondonLondonUnited Kingdom
  4. 4.Communications and Electronics DepartmentTélécom ParisTechParisFrance
  5. 5.Department of Electrical and Computer Systems EngineeringMonash UniversityClaytonAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-67882-5
  • Copyright Information The Author(s) 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-67881-8
  • Online ISBN 978-3-319-67882-5
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site