Error Correction Coding

Mathematical Methods and Algorithms

Todd K. Moon

• Publisher: Wiley
• Year: 2020
• Print ISBN: 9781119567479
• eBook ISBN: 9781119567486
• Edition: 2
• Topic: Computer Science
• Subtopic: Computer Science General
• Index: Computer Science

Providing in-depth treatment of error correction

Error Correction Coding: Mathematical Methods and Algorithms, 2nd Edition provides a comprehensive introduction to classical and modern methods of error correction. The presentation provides a clear, practical introduction to using a lab-oriented approach. Readers are encouraged to implement the encoding and decoding algorithms with explicit algorithm statements and the mathematics used in error correction, balanced with an algorithmic development on how to actually do the encoding and decoding. Both block and stream (convolutional) codes are discussed, and the mathematics required to understand them are introduced on a "just-in-time" basis as the reader progresses through the book.

The second edition increases the impact and reach of the book, updating it to discuss recent important technological advances. New material includes:

• Extensive coverage of LDPC codes, including a variety of decoding algorithms
• A comprehensive introduction to polar codes, including systematic encoding/decoding and list decoding
• An introduction to fountain codes
• Modern applications to systems such as HDTV, DVBT2, and cell phones

Error Correction Coding includes extensive program files (for example, C++ code for all LDPC decoders and polar code decoders), laboratory materials for students to implement algorithms, and an updated solutions manual, all of which are perfect to help the reader understand and retain the content.

The book covers classical BCH, Reed Solomon, Golay, Reed Muller, Hamming, and convolutional codes which are still component codes in virtually every modern communication system. There are also fulsome discussions of recently developed polar codes and fountain codes that serve to educate the reader on the newest developments in error correction.

Table of contents

• Cover
• Title Page
• Copyright
• Contents
• Preface
• List of Program Files
• List of Laboratory Exercises
• List of Algorithms
• List of Figures
• List of Tables
• List of Boxes
• About the Companion Website
• Part I Introduction and Foundations
• Chapter 1 A Context for Error Correction Coding
• Part II Block Codes
• Chapter 2 Groups and Vector Spaces
• Chapter 3 Linear Block Codes
• Chapter 4 Cyclic Codes, Rings, and Polynomials
• Chapter 5 Rudiments of Number Theory and Algebra
• Chapter 6 BCH and Reed–Solomon Codes: Designer Cyclic Codes
• Chapter 7 Alternate Decoding Algorithms for Reed–Solomon Codes
• Chapter 8 Other Important Block Codes
• Chapter 9 Bounds on Codes
• Chapter 10 Bursty Channels, Interleavers, and Concatenation
• Chapter 11 Soft‐Decision Decoding Algorithms
• Part III Codes on Graphs
• Chapter 12 Convolutional Codes
• Chapter 13 Trellis‐Coded Modulation
• Part IV Iteratively Decoded Codes
• Chapter 14 Turbo Codes
• Chapter 15 Low‐Density Parity‐Check Codes: Introduction, Decoding, and Analysis
• Chapter 16 Low‐Density Parity‐Check Codes: Designs and Variations
• Part V Polar Codes
• Chapter 17 Polar Codes
• Part VI Applications
• Chapter 18 Some Applications of Error Correction in Modern Communication Systems
• Part VII Space-Time Coding
• Chapter 19 Fading Channels and Space‐Time Codes
• References
• Index
• EULA