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

✍ Scribed by Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril (auth.)

• Publisher: Springer International Publishing
• Year: 2017
• Tongue: English
• Leaves: 527
• Series: Signals and Communication Technology
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Communications Engineering, Networks;Computer Communication Networks;Coding and Information Theory;Algorithms