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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.
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