Error Correction Coding: Mathematical Methods and Algorithms, 2nd Edition

Error Correction Coding: Mathematical Methods and Algorithms, 2nd Edition

Book Description
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. 


Part I - Introduction and Foundations
1. A Context for Error Correction Coding

Part II - Block Codes
2. Groups and Vector Spaces
3. Linear Block Codes
4. Cyclic Codes, Rings, and Polynomials
5. Rudiments of Number Theory and Algebra
6. BCH and Reed–Solomon Codes: Designer Cyclic Codes
7. Alternate Decoding Algorithms for Reed–Solomon Codes
8. Other Important Block Codes
9. Bounds on Codes
10. Bursty Channels, Interleavers, and Concatenation
11. Soft-Decision Decoding Algorithms

Part III - Codes on Graphs
12. Convolutional Codes
13. Trellis-Coded Modulation

Part IV - Iteratively Decoded Codes
14. Turbo Codes
15. Low-Density Parity-Check Codes: Introduction, Decoding, and Analysis
16. Low-Density Parity-Check Codes: Designs and Variations

Part V - Polar Codes
17. Polar Codes

Part VI - Applications
18. Some Applications of Error Correction in Modern Communication Systems

Part VII - Space-Time Coding
19. Fading Channels and Space-Time Codes

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