Lattices And Codes

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Lattice Coding for Signals and Networks

Author : Ram Zamir
Publisher : Cambridge University Press
ISBN 13 : 1139991590
Total Pages : 459 pages
Book Rating : 4.1/5 (399 download)

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Book Synopsis Lattice Coding for Signals and Networks by : Ram Zamir

Download or read book Lattice Coding for Signals and Networks written by Ram Zamir and published by Cambridge University Press. This book was released on 2014-08-07 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lattices and Codes

Author : Wolfgang Ebeling
Publisher : Vieweg+Teubner Verlag
ISBN 13 : 9783322900159
Total Pages : 188 pages
Book Rating : 4.9/5 (1 download)

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Book Synopsis Lattices and Codes by : Wolfgang Ebeling

Download or read book Lattices and Codes written by Wolfgang Ebeling and published by Vieweg+Teubner Verlag. This book was released on 2012-04-19 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 2nd edition numerous corrections have been made. More basic material has been included to make the text even more self-contained. A new section on the automorphism group of the Leech lattice has been added. Some hints to new results have been incorporated. With several new exercises.

Lattices and Codes

Author : Wolfgang Ebeling
Publisher : Springer Science & Business Media
ISBN 13 : 3658003596
Total Pages : 177 pages
Book Rating : 4.6/5 (58 download)

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Book Synopsis Lattices and Codes by : Wolfgang Ebeling

Download or read book Lattices and Codes written by Wolfgang Ebeling and published by Springer Science & Business Media. This book was released on 2013 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory. In the 3rd edition, again numerous corrections and improvements have been made and the text has been updated. Content Lattices and Codes -Theta Functions and Weight Enumerators - Even Unimodular Lattices - The Leech Lattice - Lattices over Integers of Number Fields and Self-Dual Codes. Readership Graduate Students in Mathematics and Computer Science Mathematicians and Computer Scientists About the Author Prof. Dr. Wolfgang Ebeling, Institute of Algebraic Geometry, Leibniz Universität Hannover, Germany

Sphere Packings, Lattices and Groups

Author : J.H. Conway
Publisher : Springer Science & Business Media
ISBN 13 : 1475722494
Total Pages : 724 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Sphere Packings, Lattices and Groups by : J.H. Conway

Download or read book Sphere Packings, Lattices and Groups written by J.H. Conway and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics. Results as of 1992 have been added to the text, and the extensive bibliography - itself a contribution to the field - is supplemented with approximately 450 new entries.

Self-Dual Codes and Invariant Theory

Author : Gabriele Nebe
Publisher : Springer Science & Business Media
ISBN 13 : 9783540307297
Total Pages : 474 pages
Book Rating : 4.3/5 (72 download)

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Book Synopsis Self-Dual Codes and Invariant Theory by : Gabriele Nebe

Download or read book Self-Dual Codes and Invariant Theory written by Gabriele Nebe and published by Springer Science & Business Media. This book was released on 2006-02-09 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory, which has inspired hundreds of papers about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations.

Selected Topics In Information And Coding Theory

Author : Isaac Woungang
Publisher : World Scientific
ISBN 13 : 981446919X
Total Pages : 725 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Selected Topics In Information And Coding Theory by : Isaac Woungang

Download or read book Selected Topics In Information And Coding Theory written by Isaac Woungang and published by World Scientific. This book was released on 2010-02-26 with total page 725 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last few years have witnessed rapid advancements in information and coding theory research and applications. This book provides a comprehensive guide to selected topics, both ongoing and emerging, in information and coding theory. Consisting of contributions from well-known and high-profile researchers in their respective specialties, topics that are covered include source coding; channel capacity; linear complexity; code construction, existence and analysis; bounds on codes and designs; space-time coding; LDPC codes; and codes and cryptography.All of the chapters are integrated in a manner that renders the book as a supplementary reference volume or textbook for use in both undergraduate and graduate courses on information and coding theory. As such, it will be a valuable text for students at both undergraduate and graduate levels as well as instructors, researchers, engineers, and practitioners in these fields.Supporting Powerpoint Slides are available upon request for all instructors who adopt this book as a course text.

Lattice Theory

Author : George Gratzer
Publisher : Courier Corporation
ISBN 13 : 048647173X
Total Pages : 242 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Lattice Theory by : George Gratzer

Download or read book Lattice Theory written by George Gratzer and published by Courier Corporation. This book was released on 2009-01-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding text is written in clear language and enhanced with many exercises, diagrams, and proofs. It discusses historical developments and future directions and provides an extensive bibliography and references. 1971 edition.

Number Theory Meets Wireless Communications

Author : Victor Beresnevich
Publisher : Springer Nature
ISBN 13 : 3030613038
Total Pages : 281 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Number Theory Meets Wireless Communications by : Victor Beresnevich

Download or read book Number Theory Meets Wireless Communications written by Victor Beresnevich and published by Springer Nature. This book was released on 2021-01-08 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Error-Correcting Linear Codes

Author : Anton Betten
Publisher : Springer Science & Business Media
ISBN 13 : 3540317031
Total Pages : 819 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Error-Correcting Linear Codes by : Anton Betten

Download or read book Error-Correcting Linear Codes written by Anton Betten and published by Springer Science & Business Media. This book was released on 2006-09-21 with total page 819 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The relevant algebraic are developed rigorously. Cyclic codes are discussed in great detail. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically.

Coding Theory

Author : Jacobus H. van Lint
Publisher : Springer
ISBN 13 : 3662207125
Total Pages : 145 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis Coding Theory by : Jacobus H. van Lint

Download or read book Coding Theory written by Jacobus H. van Lint and published by Springer. This book was released on 2013-12-11 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Course in Algebraic Error-Correcting Codes

Author : Simeon Ball
Publisher : Springer Nature
ISBN 13 : 3030411532
Total Pages : 185 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis A Course in Algebraic Error-Correcting Codes by : Simeon Ball

Download or read book A Course in Algebraic Error-Correcting Codes written by Simeon Ball and published by Springer Nature. This book was released on 2020-05-08 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.

Codes And Modular Forms: A Dictionary

Author : Minjia Shi
Publisher : World Scientific
ISBN 13 : 9811212937
Total Pages : 232 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Codes And Modular Forms: A Dictionary by : Minjia Shi

Download or read book Codes And Modular Forms: A Dictionary written by Minjia Shi and published by World Scientific. This book was released on 2019-11-20 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are connections between invariant theory and modular forms since the times of Felix Klein, in the 19th century, connections between codes and lattices since the 1960's. The aim of the book is to explore the interplay between codes and modular forms. Here modular form is understood in a wide sense (Jacobi forms, Siegel forms, Hilbert forms). Codes comprises not only linear spaces over finite fields but modules over some commutative rings. The connection between codes over finite fields and lattices has been well documented since the 1970s. Due to an avalanche of results on codes over rings since the 1990's there is a need for an update at book level.

Concise Encyclopedia of Coding Theory

Author : W. Cary Huffman
Publisher : CRC Press
ISBN 13 : 1351375105
Total Pages : 998 pages
Book Rating : 4.3/5 (513 download)

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Book Synopsis Concise Encyclopedia of Coding Theory by : W. Cary Huffman

Download or read book Concise Encyclopedia of Coding Theory written by W. Cary Huffman and published by CRC Press. This book was released on 2021-03-26 with total page 998 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Semimodular Lattices

Author : Manfred Stern
Publisher : Cambridge University Press
ISBN 13 : 0521461057
Total Pages : 386 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Semimodular Lattices by : Manfred Stern

Download or read book Semimodular Lattices written by Manfred Stern and published by Cambridge University Press. This book was released on 1999-05-13 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of semimodularity that presents theory and applications in discrete mathematics, group theory and universal algebra.

Quarks, Gluons and Lattices

Author : Michael Creutz
Publisher : Cambridge University Press
ISBN 13 : 100929038X
Total Pages : 179 pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis Quarks, Gluons and Lattices by : Michael Creutz

Download or read book Quarks, Gluons and Lattices written by Michael Creutz and published by Cambridge University Press. This book was released on 2023-01-31 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1983 book, reissued as OA, introduces the lattice approach to QFT for elementary particle and solid state physicists.

Advances in Cryptology -- EUROCRYPT 2012

Author : David Pointcheval
Publisher : Springer Science & Business Media
ISBN 13 : 3642290108
Total Pages : 769 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Advances in Cryptology -- EUROCRYPT 2012 by : David Pointcheval

Download or read book Advances in Cryptology -- EUROCRYPT 2012 written by David Pointcheval and published by Springer Science & Business Media. This book was released on 2012-04-02 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2012, held in Cambgridge, UK, in April 2012. The 41 papers, presented together with 2 invited talks, were carefully reviewed and selected from 195 submissions. The papers are organized in topical sections on index calculus, symmetric constructions, secure computation, protocols, lossy trapdoor functions, tools, symmetric cryptanalysis, fully homomorphic encryption, asymmetric cryptanalysis, efficient reductions, public-key schemes, security models, and lattices.

Selected Unsolved Problems in Coding Theory

Author : David Joyner
Publisher : Springer Science & Business Media
ISBN 13 : 0817682562
Total Pages : 211 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Selected Unsolved Problems in Coding Theory by : David Joyner

Download or read book Selected Unsolved Problems in Coding Theory written by David Joyner and published by Springer Science & Business Media. This book was released on 2011-08-26 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using an original mode of presentation, and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that still exist in coding theory. A well-established and highly relevant branch of mathematics, the theory of error-correcting codes is concerned with reliably transmitting data over a ‘noisy’ channel. Despite frequent use in a range of contexts, the subject still contains interesting unsolved problems that have resisted solution by some of the most prominent mathematicians of recent decades. Employing Sage—a free open-source mathematics software system—to illustrate ideas, this book is intended for graduate students and researchers in algebraic coding theory. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study.