## Fundamentals of Error Correcting Codes

Author: W. Cary Huffman
Publisher: Cambridge University Press
ISBN: 9781139439503
Format: PDF, ePub

Fundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint. As well as covering classical topics, there is much coverage of techniques which could only be found in specialist journals and book publications. Numerous exercises and examples and an accessible writing style make this a lucid and effective introduction to coding theory for advanced undergraduate and graduate students, researchers and engineers, whether approaching the subject from a mathematical, engineering or computer science background.

## Introduction to Error correcting Codes

Author: Michael Purser
Publisher: Artech House on Demand
ISBN: 9780890067840
Format: PDF, ePub, Mobi

This title covers the fundamentals of error-correcting codes for the non-specialist user, from general concepts through to the most common error-correcting codes applied to bit transmission in packet switched networks and personal cellular systems. It also includes sections on linear blockades, BCH codes and cyclic codes.

## Introduction to the Theory of Error Correcting Codes

Author: Vera Pless
Publisher: John Wiley & Sons
ISBN: 1118030990
Format: PDF, Docs

A complete introduction to the many mathematical tools used to solve practical problems in coding. Mathematicians have been fascinated with the theory of error-correcting codes since the publication of Shannon's classic papers fifty years ago. With the proliferation of communications systems, computers, and digital audio devices that employ error-correcting codes, the theory has taken on practical importance in the solution of coding problems. This solution process requires the use of a wide variety of mathematical tools and an understanding of how to find mathematical techniques to solve applied problems. Introduction to the Theory of Error-Correcting Codes, Third Edition demonstrates this process and prepares students to cope with coding problems. Like its predecessor, which was awarded a three-star rating by the Mathematical Association of America, this updated and expanded edition gives readers a firm grasp of the timeless fundamentals of coding as well as the latest theoretical advances. This new edition features: * A greater emphasis on nonlinear binary codes * An exciting new discussion on the relationship between codes and combinatorial games * Updated and expanded sections on the Vashamov-Gilbert bound, van Lint-Wilson bound, BCH codes, and Reed-Muller codes * Expanded and updated problem sets. Introduction to the Theory of Error-Correcting Codes, Third Edition is the ideal textbook for senior-undergraduate and first-year graduate courses on error-correcting codes in mathematics, computer science, and electrical engineering.

## An Introduction to Error Correcting Codes with Applications

Author: Scott A. Vanstone
Publisher: Springer Science & Business Media
ISBN: 1475720327
Format: PDF, ePub

5. 2 Rings and Ideals 148 5. 3 Ideals and Cyclic Subspaces 152 5. 4 Generator Matrices and Parity-Check Matrices 159 5. 5 Encoding Cyclic Codest 163 5. 6 Syndromes and Simple Decoding Procedures 168 5. 7 Burst Error Correcting 175 5. 8 Finite Fields and Factoring xn-l over GF(q) 181 5. 9 Another Method for Factoring xn-l over GF(q)t 187 5. 10 Exercises 193 Chapter 6 BCH Codes and Bounds for Cyclic Codes 6. 1 Introduction 201 6. 2 BCH Codes and the BCH Bound 205 6. 3 Bounds for Cyclic Codest 210 6. 4 Decoding BCH Codes 215 6. 5 Linearized Polynomials and Finding Roots of Polynomialst 224 6. 6 Exercises 231 Chapter 7 Error Correction Techniques and Digital Audio Recording 7. 1 Introduction 237 7. 2 Reed-Solomon Codes 237 7. 3 Channel Erasures 240 7. 4 BCH Decoding with Erasures 244 7. 5 Interleaving 250 7. 6 Error Correction and Digital Audio Recording 256 7.

## Error Correction Coding and Decoding

Author: Martin Tomlinson
Publisher: Springer
ISBN: 3319511033
Format: PDF

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.

## VLSI Architectures for Modern Error Correcting Codes

Author: Xinmiao Zhang
Publisher: CRC Press
ISBN: 148222965X
Format: PDF, Kindle

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.

## Error Correcting Linear Codes

Author: Anton Betten
Publisher: Springer Science & Business Media
ISBN: 3540317031
Format: PDF, Mobi

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.

## Lectures on Quantum Computation Quantum Error Correcting Codes and Information Theory

Author: K. R. Parthasarathy
Publisher: Amer Mathematical Society
ISBN:
Format: PDF, Mobi

"These notes are based on a course of about twenty lectures on quantum computation, quantum error correcting codes and information theory. Shor's Factorization algorithm, Knill-Laflamme theory of error correcting quantum codes and the basic ideas of classical and quantum information theory are discussed. The only background expected of the reader is familiarity with linear algebra in finite dimensional complex vector space and elementary probability theory."--BOOK JACKET.

## Error Coding for Engineers

Author: A. Houghton
Publisher: Springer Science & Business Media
ISBN: 9780792375227
Format: PDF, Docs

Error Coding for Engineers provides a useful tool for practicing engineers, students, and researchers, focusing on the applied rather than the theoretical. It describes the processes involved in coding messages in such a way that, if errors occur during transmission or storage, they are detected and, if necessary, corrected. Very little knowledge beyond a basic understanding of binary manipulation and Boolean algebra is assumed, making the subject accessible to a broad readership including non-specialists. The approach is tutorial: numerous examples, illustrations, and tables are included, along with over 30 pages of hands-on exercises and solutions. Error coding is essential in many modern engineering applications. Engineers involved in communications design, DSP-based applications, IC design, protocol design, storage solutions, and memory product design are among those who will find the book to be a valuable reference. Error Coding for Engineers is also suitable as a text for basic and advanced university courses in communications and engineering.

## Quantum Information Processing and Quantum Error Correction

Author: Ivan Djordjevic