Error Correction Coding - Mathematical Methods and Algorithms

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.

List of contents

Preface xvii
 
List of Program Files xxiii
 
List of Laboratory Exercises xxix
 
List of Algorithms xxxi
 
List of Figures xxxiii
 
List of Tables xli
 
List of Boxes xliii
 
About the Companion Website xlv
 
Part I Introduction and Foundations 1
 
1 A Context for Error Correction Coding 3
 
Part II Block Codes 69
 
2 Groups and Vector Spaces 71
 
3 Linear Block Codes 93
 
4 Cyclic Codes, Rings, and Polynomials 123
 
5 Rudiments of Number Theory and Algebra 179
 
6 BCH and Reed-Solomon Codes: Designer Cyclic Codes 241
 
7 Alternate Decoding Algorithms for Reed-Solomon Codes 299
 
8 Other Important Block Codes 371
 
9 Bounds on Codes 407
 
10 Bursty Channels, Interleavers, and Concatenation 425
 
11 Soft-Decision Decoding Algorithms 439
 
Part III Codes on Graphs 453
 
12 Convolutional Codes 455
 
13 Trellis-Coded Modulation 545
 
Part IV Iteratively Decoded Codes 589
 
14 Turbo Codes 591
 
15 Low-Density Parity-Check Codes: Introduction, Decoding, and Analysis 637
 
16 Low-Density Parity-Check Codes: Designs and Variations 717
 
Part V Polar Codes 777
 
17 Polar Codes 779
 
Part VI Applications 885
 
18 Some Applications of Error Correction in Modern Communication Systems 887
 
Part VII Space-Time Coding 899
 
19 Fading Channels and Space-Time Codes 901
 
References 925
 
Index 939

About the author

TODD K. MOON is a Professor in the Electrical and Computer Engineering Department at Utah State University. His research interests include information systems (communications, signal processing, and controls) and the application of principles of mathematics to problems involving the transmission, extraction, modeling, compression, or analysis of signals. He is the author of numerous journal and conference articles and graduate level texts on signal processing and error correction coding.

Summary

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.

Product details

• Authors: Tk Moon, Todd K Moon, Todd K. Moon, Moon Todd K.
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 30.11.2020
• EAN: 9781119567479
• ISBN: 978-1-119-56747-9
• No. of pages: 992
• Subjects: Natural sciences, medicine, IT, technology > Technology > Electronics, electrical engineering, communications engineering; Informatik, informationstechnologie, Signalverarbeitung, computer science, drahtlose kommunikation, Signal Processing, Information Technologies, Electrical & Electronics Engineering, Elektrotechnik u. Elektronik