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 "e;just-in-time"e; 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.

Providing in-depth treatment of error correctionError 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 phonesError 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 xviiList of Program Files xxiiiList of Laboratory Exercises xxixList of Algorithms xxxiList of Figures xxxiiiList of Tables xliList of Boxes xliiiAbout the Companion Website xlvPart I Introduction and Foundations 11 A Context for Error Correction Coding 3Part II Block Codes 692 Groups and Vector Spaces 713 Linear Block Codes 934 Cyclic Codes, Rings, and Polynomials 1235 Rudiments of Number Theory and Algebra 1796 BCH and Reed-Solomon Codes: Designer Cyclic Codes 2417 Alternate Decoding Algorithms for Reed-Solomon Codes 2998 Other Important Block Codes 3719 Bounds on Codes 40710 Bursty Channels, Interleavers, and Concatenation 42511 Soft-Decision Decoding Algorithms 439Part III Codes on Graphs 45312 Convolutional Codes 45513 Trellis-Coded Modulation 545Part IV Iteratively Decoded Codes 58914 Turbo Codes 59115 Low-Density Parity-Check Codes: Introduction, Decoding, and Analysis 63716 Low-Density Parity-Check Codes: Designs and Variations 717Part V Polar Codes 77717 Polar Codes 779Part VI Applications 88518 Some Applications of Error Correction in Modern Communication Systems 887Part VII Space-Time Coding 89919 Fading Channels and Space-Time Codes 901Index 939