Lattices Applied to Coding for Reliable and Secure Communications
Lattices Applied to Coding for Reliable and Secure Communications

Author: Sueli I.R. Costa

Publisher: Springer

Published: 2018-04-02

Total Pages: 123

ISBN-13: 3319678825

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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.

Public-Key Cryptography – PKC 2023
Public-Key Cryptography – PKC 2023

Author: Alexandra Boldyreva

Publisher: Springer Nature

Published: 2023-05-01

Total Pages: 812

ISBN-13: 3031313682

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The two-volume proceedings set LNCS 13940 and 13941 constitutes the refereed proceedings of the 26th IACR International Conference on Practice and Theory of Public Key Cryptography, PKC 2023, which took place in March 2023 in Atlanta, GA, USA. The 49 papers included in these proceedings were carefully reviewed and selected from 183 submissions. They focus on all aspects of public-key cryptography, covering Post-Quantum Cryptography, Key Exchange and Messaging, Encryption, Homomorphic Cryptography and other topics.

Concise Encyclopedia of Coding Theory
Concise Encyclopedia of Coding Theory

Author: W. Cary Huffman

Publisher: CRC Press

Published: 2021-03-26

Total Pages: 998

ISBN-13: 1351375105

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Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research

Advances in Mathematics and Applications
Advances in Mathematics and Applications

Author: Carlile Lavor

Publisher: Springer

Published: 2018-09-07

Total Pages: 408

ISBN-13: 3319940155

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This book celebrates the 50th anniversary of the Institute of Mathematics, Statistics and Scientific Computing (IMECC) of the University of Campinas, Brazil, by offering reviews of selected research developed at one of the most prestigious mathematics institutes in Latin America. Written by senior professors at the IMECC, it covers topics in pure and applied mathematics and statistics ranging from differential geometry, dynamical systems, Lie groups, and partial differential equations to computational optimization, mathematical physics, stochastic process, time series, and more. A report on the challenges and opportunities of research in applied mathematics - a highly active field of research in the country - and highlights of the Institute since its foundation in 1968 completes this historical volume, which is unveiled in the same year that the International Mathematical Union (IMU) names Brazil as a member of the Group V of countries with the most relevant contributions in mathematics.

Number Theory Meets Wireless Communications
Number Theory Meets Wireless Communications

Author: Victor Beresnevich

Publisher: Springer Nature

Published: 2021-01-08

Total Pages: 281

ISBN-13: 3030613038

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This volume explores the rich interplay between number theory and wireless communications, reviewing the surprisingly deep connections between these fields and presenting new research directions to inspire future research. The contributions of this volume stem from the Workshop on Interactions between Number Theory and Wireless Communication held at the University of York in 2016. The chapters, written by leading experts in their respective fields, provide direct overviews of highly exciting current research developments. The topics discussed include metric Diophantine approximation, geometry of numbers, homogeneous dynamics, algebraic lattices and codes, network and channel coding, and interference alignment. The book is edited by experts working in number theory and communication theory. It thus provides unique insight into key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research. Great effort has been made to present the material in a manner that is accessible to new researchers, including PhD students. The book will also be essential reading for established researchers working in number theory or wireless communications looking to broaden their outlook and contribute to this emerging interdisciplinary area.

Algebra for Secure and Reliable Communication Modeling
Algebra for Secure and Reliable Communication Modeling

Author: Mustapha Lahyane

Publisher: American Mathematical Soc.

Published: 2015-06-23

Total Pages: 258

ISBN-13: 1470410184

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This volume contains the proceedings of the CIMPA Research School and Conference on Algebra for Secure and Reliable Communication Modeling, held from October 1-13, 2012, in Morelia, State of Michoacán, Mexico. The papers cover several aspects of the theory of coding theory and are gathered into three categories: general theory of linear codes, algebraic geometry and coding theory, and constacyclic codes over rings. The aim of this volume is to fill the gap between the theoretical part of algebraic geometry and the applications to problem solving and computational modeling in engineering, signal processing and information theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).

Physical Layer Security for 6G
Physical Layer Security for 6G

Author: Parthajit Mohapatra

Publisher: John Wiley & Sons

Published: 2024-11-13

Total Pages: 389

ISBN-13: 1394170912

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Meet the wireless security challenges of the future with this key volume The 6th generation of wireless communication technology—known as 6G—promises to bring both revolutionary advances and unique challenges. Secure communications will be harder than ever to achieve under the new integrated ground, air, and space networking paradigm; increased connectivity creates the potential for increased vulnerability. Physical layer security, which draws upon the physical properties of the channel or network to secure information, has emerged as a promising solution to these challenges. Physical Layer Security for 6G provides a working introduction to these technologies and their burgeoning wireless applications. With particular attention to heterogeneous or distributed network scenarios, this book offers both the information-theory fundamentals and the most recent developments in physical layer security. It constitutes an essential resource for meeting the unique security challenges of 6G. Physical Layer Security for 6G readers will also find: Analysis of physical layer security in the quality of security framework (QoSec) Detailed discussion of physical layer security applications in visible light communication (VLC), intelligence reflecting surface (IRS), and more Practical use cases and demonstrations Physical Layer Security for 6G is ideal for wireless research engineers as well as advanced graduate students in wireless technology.

Applied Coding and Information Theory for Engineers
Applied Coding and Information Theory for Engineers

Author: Richard B. Wells

Publisher: Pearson

Published: 1999

Total Pages: 0

ISBN-13: 9780139613272

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This book provides a practical introduction to the theory and practice of coding and information theory for application in the field of electronic communications. It is written at an introductory level and assumes no prior background in coding or information theory. While the mathematical level is detailed, it is still introductory. Through a discussion that balances theory and practical applications and abandons the traditional "theorem-proof" format, this valuable book presents an overview of digital communication systems and the concept of information. It is written in a easy-to-follow conversational style that integrates practical engineering issues through formal and conceptual discussions of mathematical issues. It also makes extensive use of explicit examples that illustrate methods and theory throughout the book. For the professional, it provides an essential hands-on head start for real-world projects and situations. An essential reference for professional engineers in the field of electronic communications.

Lattice Coding for Signals and Networks
Lattice Coding for Signals and Networks

Author: Ram Zamir

Publisher: Cambridge University Press

Published: 2014-08-07

Total Pages: 459

ISBN-13: 1139991590

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Unifying information theory and digital communication through the language of lattice codes, this book provides a detailed overview for students, researchers and industry practitioners. It covers classical work by leading researchers in the field of lattice codes and complementary work on dithered quantization and infinite constellations, and then introduces the more recent results on 'algebraic binning' for side-information problems, and linear/lattice codes for networks. It shows how high dimensional lattice codes can close the gap to the optimal information theoretic solution, including the characterisation of error exponents. The solutions presented are based on lattice codes, and are therefore close to practical implementations, with many advanced setups and techniques, such as shaping, entropy-coding, side-information and multi-terminal systems. Moreover, some of the network setups shown demonstrate how lattice codes are potentially more efficient than traditional random-coding solutions, for instance when generalising the framework to Gaussian networks.