Error Correction Coding

Error Correction Coding
Author: Todd K. Moon
Publisher: John Wiley & Sons
Total Pages: 999
Release: 2020-12-22
Genre: Computers
ISBN: 1119567475

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.

Introduction to Global Variational Geometry

Introduction to Global Variational Geometry
Author: Demeter Krupka
Publisher: Elsevier
Total Pages: 787
Release: 2000-04-01
Genre: Mathematics
ISBN: 0080954235

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether's theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles- First book on the geometric foundations of Lagrange structures- New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity- Basic structures and tools: global analysis, smooth manifolds, fibred spaces

Error-Correction Coding for Digital Communications

Error-Correction Coding for Digital Communications
Author: George C. Clark Jr.
Publisher: Springer Science & Business Media
Total Pages: 452
Release: 1981-06-30
Genre: Technology & Engineering
ISBN: 9780306406157

Error-correction coding is being used on an almost routine basis in most new communication systems. Not only is coding equipment being used to increase the energy efficiency of communication links, but coding ideas are also providing innovative solutions to many related communication problems. Among these are the elimination of intersymbol interference caused by filtering and multipath and the improved demodulation of certain frequency modulated signals by taking advantage of the "natural" coding provided by a continuous phase. Although several books and nu merous articles have been written on coding theory, there are still noticeable deficiencies. First, the practical aspects of translating a specific decoding algorithm into actual hardware have been largely ignored. The information that is available is sketchy and is widely dispersed. Second, the information required to evaluate a particular technique under situations that are en countered in practice is available for the most part only in private company reports. This book is aimed at correcting both of these problems. It is written for the design engineer who must build the coding and decoding equipment and for the communication system engineer who must incorporate this equipment into a system. It is also suitable as a senior-level or first-year graduate text for an introductory one-semester course in coding theory. The book U"Ses a minimum of mathematics and entirely avoids the classical theorem/proof approach that is often seen in coding texts.

Understanding Error Control Coding

Understanding Error Control Coding
Author: Emilio Sanvicente
Publisher: Springer
Total Pages: 324
Release: 2019-04-10
Genre: Technology & Engineering
ISBN: 3030058409

This book is addressed to newcomers to error control coding (ECC), making the subject easy to understand and to apply in a variety of cases. The book begins by presenting in a detailed, step-by-step manner the plethora of parts an ECC system has and the way they interact to achieve the performance required. Contrary to the more abstract and formal approach followed in most books on this topic, this book is unique in that all of the concepts, methods, techniques and algorithms are introduced by way of examples. Thus, the book is almost a workbook, and therefore very suitable for self-study. Readers are encouraged to take an active role while reading, performing calculations as chapters’ progress. Moreover, to reinforce the learning process, many of the topics introduced in the book (Galois fields, Extended Hamming codes, Reed-Solomon codes, interleaving, erasure correction, etc.) are presented in various parts of the book in different ways or contexts. Offers a practical guide to error control coding, accessible to readers with varying backgrounds; Provides newcomers with a sound foundation in error control coding, using a select few topics considered by the author fundamental from an engineering point of view; Presents material with minimal mathematics; Motivates carefully concepts, methods and algorithms making clear the idea behind the conditions for the code to work.

VLSI Architectures for Modern Error-Correcting Codes

VLSI Architectures for Modern Error-Correcting Codes
Author: Xinmiao Zhang
Publisher: CRC Press
Total Pages: 387
Release: 2017-12-19
Genre: Technology & Engineering
ISBN: 1351831224

Error-correcting codes are ubiquitous. They are adopted in almost every modern digital communication and storage system, such as wireless communications, optical communications, Flash memories, computer hard drives, sensor networks, and deep-space probing. New-generation and emerging applications demand codes with better error-correcting capability. On the other hand, the design and implementation of those high-gain error-correcting codes pose many challenges. They usually involve complex mathematical computations, and mapping them directly to hardware often leads to very high complexity. VLSI Architectures for Modern Error-Correcting Codes serves as a bridge connecting advancements in coding theory to practical hardware implementations. Instead of focusing on circuit-level design techniques, the book highlights integrated algorithmic and architectural transformations that lead to great improvements on throughput, silicon area requirement, and/or power consumption in the hardware implementation. The goal of this book is to provide a comprehensive and systematic review of available techniques and architectures, so that they can be easily followed by system and hardware designers to develop en/decoder implementations that meet error-correcting performance and cost requirements. This book can be also used as a reference for graduate-level courses on VLSI design and error-correcting coding. Particular emphases are placed on hard- and soft-decision Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) codes, and binary and non-binary low-density parity-check (LDPC) codes. These codes are among the best candidates for modern and emerging applications due to their good error-correcting performance and lower implementation complexity compared to other codes. To help explain the computations and en/decoder architectures, many examples and case studies are included. More importantly, discussions are provided on the advantages and drawbacks of different implementation approaches and architectures.

Code Design for Dependable Systems

Code Design for Dependable Systems
Author: Eiji Fujiwara
Publisher: John Wiley & Sons
Total Pages: 718
Release: 2006-05-26
Genre: Science
ISBN: 047179273X

Theoretical and practical tools to master matrix code design strategy and technique Error correcting and detecting codes are essential to improving system reliability and have popularly been applied to computer systems and communication systems. Coding theory has been studied mainly using the code generator polynomials; hence, the codes are sometimes called polynomial codes. On the other hand, the codes designed by parity check matrices are referred to in this book as matrix codes. This timely book focuses on the design theory for matrix codes and their practical applications for the improvement of system reliability. As the author effectively demonstrates, matrix codes are far more flexible than polynomial codes, as they are capable of expressing various types of code functions. In contrast to other coding theory publications, this one does not burden its readers with unnecessary polynomial algebra, but rather focuses on the essentials needed to understand and take full advantage of matrix code constructions and designs. Readers are presented with a full array of theoretical and practical tools to master the fine points of matrix code design strategy and technique: * Code designs are presented in relation to practical applications, such as high-speed semiconductor memories, mass memories of disks and tapes, logic circuits and systems, data entry systems, and distributed storage systems * New classes of matrix codes, such as error locating codes, spotty byte error control codes, and unequal error control codes, are introduced along with their applications * A new parallel decoding algorithm of the burst error control codes is demonstrated In addition to the treatment of matrix codes, the author provides readers with a general overview of the latest developments and advances in the field of code design. Examples, figures, and exercises are fully provided in each chapter to illustrate concepts and engage the reader in designing actual code and solving real problems. The matrix codes presented with practical parameter settings will be very useful for practicing engineers and researchers. References lead to additional material so readers can explore advanced topics in depth. Engineers, researchers, and designers involved in dependable system design and code design research will find the unique focus and perspective of this practical guide and reference helpful in finding solutions to many key industry problems. It also can serve as a coursebook for graduate and advanced undergraduate students.

Introduction to Error Control Codes

Introduction to Error Control Codes
Author: Salvatore Gravano
Publisher: OUP Oxford
Total Pages: 290
Release: 2001
Genre: Computers
ISBN:

This textbook provides a firm foundation for those studying the field of error control codes. giving step-by-step instruction on this complex topic beginning with single parity code checks and repetition codes. Through these basic error-control mechanisms the fundamental principles of error detection and correction, minimum distance and error-control limits are considered. With the use of detailed examples it guides students from basic error-control codes through linear codes, cyclic codes, linear feedback shift registers, vector fields, Galois fields, BCH codes and convolutional codes. There are many detailed examples throughout the book to illustrate the principles and complex mathematical proofs are omitted where possible to keep the text concise and easy-to-follow.

Additive Cellular Automata

Additive Cellular Automata
Author: Parimal Pal Chaudhuri
Publisher: John Wiley & Sons
Total Pages: 372
Release: 1997-07-11
Genre: Technology & Engineering
ISBN: 9780818677175

This book presents an extensive survey and report of related research on important developments in cellular automata (CA) theory. The authors introduce you to this theory in a comprehensive manner that will help you understand the basics of CA and be prepared for further research. They illustrate the matrix algebraic tools that characterize group CA and help develop its applications in the field of VLSI testing. The text examines schemes based on easily testable FSM, bit-error correcting code, byte error correcting code, and characterization of 2D cellular automata. In addition, it looks into CA-based universal pattern generation, data encryption, and synthesis of easily testable combinational logic. The book covers new characterizations of group CA behavior, CA-based tools for fault diagnosis, and a wide variety of applications to solve real-life problems.