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 these 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.
About the Author
Professor Martin Tomlinson is best known for inventing the Tomlinson-Harashima pre-coding technique. He received his PhD on the subject of adaptive equalisation for data transmission from Loughborough University in 1970. He later worked at Plessey Telecommunications Research Ltd. in the field of digital and satellite transmissions and then at the Satellite Communications Division of the Royal Signals and Radar Establishment (RSRE) (now Qinetiq). He was also the project manager for the communications aspects of the NATO IV satellite before joining the University of Plymouth as the head of the Communication Engineering Department in 1982. Professor Tomlinson has published 186 papers, holds 33 patents and is a well known member of several professional institutes and societies. He is Emeritus Professor of Communications at the University of Plymouth and is also Chief Scientific Officer of Post-Quantum, a company specializing in secure communications and cryptographic products.
Dr. Cen Jung Tjhai is an expert in error correcting codes, cryptography, digital signal processing and wireless communications. He is Chief Technology Officer at Post-Quantum and is responsible for secure messaging, authentication and blockchain product developments. Prior to this, he was a lecturer at the University of Plymouth and carried out research in a number of government projects in secure digital signal processing and cyber security. Dr. Tjhai has published over 30 papers and currently holds 16 patents.
Dr. Adrian Ambroze was awarded his PhD in Turbo Codes from the University of Plymouth in 2000 and currently holds the position of Lecturer in Digital Communications. He is an expert on Turbo codes, LDPC codes and iterative decoders. He is a member of the Institute of Electrical and Electronics Engineers (IEEE) and a reviewer for a number of the institute’s publications as well as for the Engineering and Physical Sciences Research Council (EPSRC). Dr. Ambrozehas published over 50 papers and currently holds 6 patents.
Dr. Zaki Ahmed completed his BEng, MEng and PhD degrees at the University of Plymouth (1996–2003) and was appointed as a permanent member of staff in 2001. He currently holds the position of Associate Professor in Information Technology and is a fellow of the Japanese Society for the Promotion of Science (FJSPS) and the Higher Education Academy (FHEA). Dr. Ahmed is also a respected member of the Institute of Electrical and Electronics Engineers. He is an expert in the areas of coding bounds and constructions of best known, error correcting codes. Dr. Ahmed has published over 70 papers and currently holds 10 patents.
Dr. Mubarak Jibril received a Bachelor of Engineering in Electrical and Electronic Engineering from Bayero University Kano in 2005. At the University of Plymouth he completed his MSc in Digital Communications and Signal Processingin 2008 and was awarded his PhD for research into Algebraic Geometry Codes in 2011. He is currently employed by the Nigerian Communications Satellite Company Limited in Abuja, Nigeria. Dr. Jibril is an expert in Algebraic Geometry (AG) error correcting codes and has published several journal articles on Goppa codes and new, best known, AG codes.
Table of Contents
Part I: Theoretical Performance of Error-Correcting Codes.- Bounds on Error Correction Coding Performance.- Soft and Hard Decision Decoding Performance.- Soft Decision and Quantised Soft Decision Decoding.- Part II: Code Construction.- Cyclotomic Cosets, The Mattson–Solomon Polynomial, Idempotents and Cyclic Codes.- Good Binary Linear Codes.- Lagrange Codes.- Extended BCH.- Reed–Solomon Codes.- Algebraic Geometry Codes.- Algebraic Quasi Cyclic Codes.- Convolutional Codes: A Historical Perspective.- Aalogue BCH Codes.- LDPC Codes.- Part III: Analysis of Codes.- True Search for Stopping Sets for LDPC Codes.- Part IV: Decoders.- Erasures and Error-Correcting Codes.- The Modified Dorsch Decoder.- A Concatenated Error-Correction System Using the |u|u+v| Code Construction.- Part V: Applications.- Combined Error Detection and Error Correction.- Password Correction and Confidential Information Access System.- Variations on the McEliece Public Key Encryption System.- Error-Correcting Codes and Dirty-Paper Coding.