Error Correction Coding

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.

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 Index 939