Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications

Description

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. Front Matter....Pages i-xx Front Matter....Pages 1-1 Bounds on Error-Correction Coding Performance....Pages 3-23 Soft and Hard Decision Decoding Performance....Pages 25-41 Soft Decision and Quantised Soft Decision Decoding....Pages 43-58 Front Matter....Pages 59-59 Cyclotomic Cosets, the Mattson–Solomon Polynomial, Idempotents and Cyclic Codes....Pages 61-99 Good Binary Linear Codes....Pages 101-136 Lagrange Codes....Pages 137-165 Reed–Solomon Codes and Binary Transmission....Pages 167-179 Algebraic Geometry Codes....Pages 181-203 Algebraic Quasi Cyclic Codes....Pages 205-288 Historical Convolutional Codes as Tail-Biting Block Codes....Pages 289-298 Analogue BCH Codes and Direct Reduced Echelon Parity Check Matrix Construction....Pages 299-314 LDPC Codes....Pages 315-354 Front Matter....Pages 355-355 An Exhaustive Tree Search for Stopping Sets of LDPC Codes....Pages 357-366 Erasures and Error-Correcting Codes....Pages 367-398 The Modified Dorsch Decoder....Pages 399-419 A Concatenated Error-Correction System Using the \(|u|u+v|\) Code Construction....Pages 421-431 Front Matter....Pages 433-434 Combined Error Detection and Error-Correction....Pages 435-450 Password Correction and Confidential Information Access System....Pages 451-463 Variations on the McEliece Public Key Cryptoystem....Pages 465-510 Error-Correcting Codes and Dirty Paper Coding....Pages 511-520 Back Matter....Pages 521-522