Fundamentals of Classical and Modern Error-Correcting Codes

Shu Lin, Juane Li

• Publisher: Cambridge University Press
• Year: 2021
• Print ISBN:
  9781316512623
• eBook ISBN:
  9781009080569
• Topic: Technology & Engineering
• Subtopic: Signals & Signal Processing
• Index: Technology & Engineering

Using easy-to-follow mathematics, this textbook provides comprehensive coverage of block codes and techniques for reliable communications and data storage. It covers major code designs and constructions from geometric, algebraic, and graph-theoretic points of view, decoding algorithms, error control additive white Gaussian noise (AWGN) and erasure, and dataless recovery. It simplifies a highly mathematical subject to a level that can be understood and applied with a minimum background in mathematics, provides step-by-step explanation of all covered topics, both fundamental and advanced, and includes plenty of practical illustrative examples to assist understanding. Numerous homework problems are included to strengthen student comprehension of new and abstract concepts, and a solutions manual is available online for instructors. Modern developments, including polar codes, are also covered. An essential textbook for senior undergraduates and graduates taking introductory coding courses, students taking advanced full-year graduate coding courses, and professionals working on coding for communications and data storage.

Table of contents

• Cover
• Half-title
• Title page
• Copyright information
• Contents
• List of Figures
• List of Tables
• Preface
• Acknowledgments
• 1 Coding for Reliable Digital Information Transmission and Storage
• 2 Some Elements of Modern Algebra and Graphs
• 3 Linear Block Codes
• 4 Binary Cyclic Codes
• 5 BCH Codes
• 6 Nonbinary BCH Codes and Reed–Solomon Codes
• 7 Finite Geometries, Cyclic Finite-Geometry Codes, and Majority-Logic Decoding
• 8 Reed–Muller Codes
• 9 Some Coding Techniques
• 10 Correction of Error-Bursts and Erasures
• 11 Introduction to Low-Density Parity-Check Codes
• 12 Cyclic and Quasi-cyclic LDPC Codes on Finite Geometries
• 13 Partial Geometries and Their Associated QC-LDPC Codes
• 14 Quasi-cyclic LDPC Codes Based on Finite Fields
• 15 Graph-Theoretic LDPC Codes
• 16 Collective Encoding and Soft-Decision Decoding of Cyclic Codes of Prime Lengths in Galois Fourier Transform Domain
• 17 Polar Codes
• Appendix A Factorization of X[sup(n)] +1 over GF(2)
• Appendix B A 2 2/3 3 SM-Constrained Masked Matrix Search Algorithm
• Appendix C Proof of Theorem 14.4
• Appendix D The 2 × 2 CPM-Array Cycle Structure of the Tanner Graph of C[sub(RS,n)](2,n)
• Appendix E Iterative Decoding Algorithm for Nonbinary LDPC Codes
• Index