Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes.

After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes. It then examines codes based on the Galois field theory as well as their application in BCH and especially the Reed–Solomon codes that have been used for error correction of data transmissions in space missions.

The major outlook in coding theory seems to be geared toward stochastic processes, and this book takes a bold step in this direction. As research focuses on error correction and recovery of erasures, the book discusses belief propagation and distributions. It examines the low-density parity-check and erasure codes that have opened up new approaches to improve wide-area network data transmission. It also describes modern codes, such as the Luby transform and Raptor codes, that are enabling new directions in high-speed transmission of very large data to multiple users.

This robust, self-contained text fully explains coding problems, illustrating them with more than 200 examples. Combining theory and computational techniques, it will appeal not only to students but also to industry professionals, researchers, and academics in areas such as coding theory and signal and image processing.

chapter 1|14 pages

Historical Background

chapter 2|28 pages

Digital Arithmetic

chapter 3|32 pages

Linear Codes

chapter 4|20 pages

Hamming Codes

chapter 5|22 pages

Extended Hamming Codes

chapter 6|26 pages

Bounds in Coding Theory

chapter 7|18 pages

Golay Codes

chapter 8|20 pages

Galois Fields

chapter 9|22 pages

Matrix Codes

chapter 10|14 pages

Cyclic Codes

chapter 11|14 pages

BCH Codes

chapter 12|26 pages

Reed−Muller Codes

chapter 13|30 pages

Reed–Solomon Codes

chapter 14|20 pages

Belief Propagation

chapter 15|20 pages

LDPC Codes

chapter 16|28 pages

Special LDPC Codes

chapter 17|20 pages

Discrete Distributions

chapter 18|20 pages

Erasure Codes

chapter 19|16 pages

Luby Transform Codes

chapter 20|16 pages

Raptor Codes

chapter |4 pages


chapter |10 pages

B Some Useful Groups

chapter C|6 pages

C Tables in Finite Fields

chapter |10 pages

D Discrete Fourier Transform

chapter |4 pages

E Software Resources