Download or read book Applied Algebra Algebraic Algorithms and Error Correcting Codes written by Marc Fossorier and published by Springer. This book was released on 2003-08-03 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-15, held in Toulouse, France, in May 2003.The 25 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 40 submissions. Among the subjects addressed are block codes; algebra and codes: rings, fields, and AG codes; cryptography; sequences; decoding algorithms; and algebra: constructions in algebra, Galois groups, differential algebra, and polynomials.

Download or read book Error Correction Coding and Decoding written by Martin Tomlinson and published by Springer. This book was released on 2017-02-21 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses both the theory and practical applications of self-correcting data, commonly known as error-correcting codes. The applications included demonstrate the importance of these codes in a wide range of everyday technologies, from smartphones to secure communications and transactions. Written in a readily understandable style, the book presents the authors’ twenty-five years of research organized into five parts: Part I is concerned with the theoretical performance attainable by using error correcting codes to achieve communications efficiency in digital communications systems. Part II explores the construction of error-correcting codes and explains the different families of codes and how they are designed. Techniques are described for producing the very best codes. Part III addresses the analysis of low-density parity-check (LDPC) codes, primarily to calculate their stopping sets and low-weight codeword spectrum which determines the performance of th ese codes. Part IV deals with decoders designed to realize optimum performance. Part V describes applications which include combined error correction and detection, public key cryptography using Goppa codes, correcting errors in passwords and watermarking. This book is a valuable resource for anyone interested in error-correcting codes and their applications, ranging from non-experts to professionals at the forefront of research in their field. This book is open access under a CC BY 4.0 license.

Download or read book Finite Geometry Low Density Parity Check Codes written by Yu Kou and published by . This book was released on 2001 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Codes Graphs and Systems written by Richard E. Blahut and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foreword by James L. Massey. Codes, Graphs, and Systems is an excellent reference for both academic researchers and professional engineers working in the fields of communications and signal processing. A collection of contributions from world-renowned experts in coding theory, information theory, and signal processing, the book provides a broad perspective on contemporary research in these areas. Survey articles are also included. Specific topics covered include convolutional codes and turbo codes; detection and equalization; modems; physics and information theory; lattices and geometry; and behaviors and codes on graphs. Codes, Graphs, and Systems is a tribute to the leadership and profound influence of G. David Forney, Jr. The 35 contributors to the volume have assembled their work in his honor.

Download or read book Channel Codes written by William Ryan and published by Cambridge University Press. This book was released on 2009-09-17 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: Channel coding lies at the heart of digital communication and data storage, and this detailed introduction describes the core theory as well as decoding algorithms, implementation details, and performance analyses. In this book, Professors Ryan and Lin provide clear information on modern channel codes, including turbo and low-density parity-check (LDPC) codes. They also present detailed coverage of BCH codes, Reed-Solomon codes, convolutional codes, finite geometry codes, and product codes, providing a one-stop resource for both classical and modern coding techniques. Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then extend to advanced topics such as code ensemble performance analyses and algebraic code design. 250 varied and stimulating end-of-chapter problems are also included to test and enhance learning, making this an essential resource for students and practitioners alike.

Download or read book LDPC Code Designs Constructions and Unification written by Juane Li and published by Cambridge University Press. This book was released on 2017 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, leading authorities unify algebraic- and graph-based LDPC code designs and constructions into a single theoretical framework.

Download or read book Low Density Parity Check Codes Based on Finite Geometries written by National Aeronautics and Space Adm Nasa and published by . This book was released on 2018-09-15 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.Kou, Yu and Lin, Shu and Fossorier, MarcGoddard Space Flight CenterEUCLIDEAN GEOMETRY; ALGORITHMS; DECODING; PARITY; ALGEBRA; INFORMATION THEORY; PROJECTIVE GEOMETRY; TWO DIMENSIONAL MODELS; COMPUTERIZED SIMULATION; ERRORS; BLOCK DIAGRAMS...

Download or read book Codes on Finite Geometries written by Heng Tang and published by . This book was released on 2002 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Construction of Structured Low density Parity check Codes written by Lei Chen and published by . This book was released on 2005 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quantum Communication Quantum Networks and Quantum Sensing written by Ivan B. Djordjevic and published by Academic Press. This book was released on 2022-07-17 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Communication, Quantum Networks, and Quantum Sensing represents a self-contained introduction to quantum communication, quantum error-correction, quantum networks, and quantum sensing. It starts with basic concepts from classical detection theory, information theory, and channel coding fundamentals before continuing with basic principles of quantum mechanics including state vectors, operators, density operators, measurements, and dynamics of a quantum system. It continues with fundamental principles of quantum information processing, basic quantum gates, no-cloning and theorem on indistinguishability of arbitrary quantum states. The book then focuses on quantum information theory, quantum detection and Gaussian quantum information theories, and quantum key distribution (QKD). The book then covers quantum error correction codes (QECCs) before introducing quantum networks. The book concludes with quantum sensing and quantum radars, quantum machine learning and fault-tolerant quantum error correction concepts. - Integrates quantum information processing fundamentals, quantum communication, quantum error correction, quantum networks, QKD, quantum sensing, and quantum machine learning - Provides in-depth exposition on the design of quantum error correction circuits, quantum communications systems, quantum networks, and quantum sensing systems - Shows how to design the information processing circuits, stabilizer codes, CSS codes, entanglement-assisted quantum error correction codes - Describes quantum machine learning

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

Download or read book Algebra and Its Applications written by D. V. Huynh and published by American Mathematical Soc.. This book was released on 2006 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of contributions by speakers at a Conference on Algebra and its Applications that took place in Athens, Ohio, in March of 2005. It provides a snapshot of the diversity of themes and applications that interest algebraists today. The papers in this volume include some of the latest results in the theory of modules, noncommutative rings, representation theory, matrix theory, linear algebra over noncommutative rings, cryptography, error-correcting codes over finite rings, and projective-geometry codes, as well as expository articles that will provide algebraists and other mathematicians, including graduate students, with an accessible introduction to areas outside their own expertise. The book will serve both the specialist looking for the latest result and the novice seeking an accessible reference for some of the ideas and results presented here.

Download or read book Error Correction Coding written by Todd K. Moon and published by John Wiley & Sons. This book was released on 2020-12-07 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing in-depth treatment of error correction Error Correction Coding: Mathematical Methods and Algorithms, 2nd Edition provides a comprehensive introduction to classical and modern methods of error correction. The presentation provides a clear, practical introduction to using a lab-oriented approach. Readers are encouraged to implement the encoding and decoding algorithms with explicit algorithm statements and the mathematics used in error correction, balanced with an algorithmic development on how to actually do the encoding and decoding. Both block and stream (convolutional) codes are discussed, and the mathematics required to understand them are introduced on a “just-in-time” basis as the reader progresses through the book. The second edition increases the impact and reach of the book, updating it to discuss recent important technological advances. New material includes: Extensive coverage of LDPC codes, including a variety of decoding algorithms. A comprehensive introduction to polar codes, including systematic encoding/decoding and list decoding. An introduction to fountain codes. Modern applications to systems such as HDTV, DVBT2, and cell phones Error Correction Coding includes extensive program files (for example, C++ code for all LDPC decoders and polar code decoders), laboratory materials for students to implement algorithms, and an updated solutions manual, all of which are perfect to help the reader understand and retain the content. The book covers classical BCH, Reed Solomon, Golay, Reed Muller, Hamming, and convolutional codes which are still component codes in virtually every modern communication system. There are also fulsome discussions of recently developed polar codes and fountain codes that serve to educate the reader on the newest developments in error correction.

Download or read book Modulation and Coding Techniques in Wireless Communications written by Evgenii Krouk and published by John Wiley & Sons. This book was released on 2011-02-21 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: The high level of technical detail included in standards specifications can make it difficult to find the correlation between the standard specifications and the theoretical results. This book aims to cover both of these elements to give accessible information and support to readers. It explains the current and future trends on communication theory and shows how these developments are implemented in contemporary wireless communication standards. Examining modulation, coding and multiple access techniques, the book is divided into two major sections to cover these functions. The two-stage approach first treats the basics of modulation and coding theory before highlighting how these concepts are defined and implemented in modern wireless communication systems. Part 1 is devoted to the presentation of main L1 procedures and methods including modulation, coding, channel equalization and multiple access techniques. In Part 2, the uses of these procedures and methods in the wide range of wireless communication standards including WLAN, WiMax, WCDMA, HSPA, LTE and cdma2000 are considered. An essential study of the implementation of modulation and coding techniques in modern standards of wireless communication Bridges the gap between the modulation coding theory and the wireless communications standards material Divided into two parts to systematically tackle the topic - the first part develops techniques which are then applied and tailored to real world systems in the second part Covers special aspects of coding theory and how these can be effectively applied to improve the performance of wireless communications systems

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.

Download or read book NeutroGeometry NeutroAlgebra and SuperHyperAlgebra in Today s World written by Smarandache, Florentin and published by IGI Global. This book was released on 2023-05-15 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: NeutroAlgebra and AntiAlgebra were extended to NeutroGeometry and AntiGeometry in order to catch the Non-Euclidean Geometries. In the real world, the spaces and the elements that populate them and the rules that apply to them are not perfect, uniform, homogeneous, or complete. They are fragmentary and disparate, with unclear and conflicting information, and they do not apply in the same degree to each element. Therefore, these partial, hybrid, and mixed structures are necessary. NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World presents applications of many NeutroStructures in our real world and considers NeutroGeometry and AntiGeometry as new fields of research that resemble everyday life. Covering key topics such as hyperbolic geometry, elliptic geometry, and AntiGeometry, this reference work is ideal for mathematicians, industry professionals, researchers, scholars, academicians, practitioners, instructors, and students.

Download or read book Fundamentals of Classical and Modern Error Correcting Codes written by Shu Lin and published by Cambridge University Press. This book was released on 2021-12-09 with total page 843 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible textbook that uses step-by-step explanations, relatively easy mathematics and numerous examples to aid student understanding.