Lattices Applied to Coding for Reliable and Secure Communications [Paperback]

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.

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

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, T?l?com 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 Univeló$