Информатика и вычислительная техника
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Lin S., Costello D. Error Control Coding Fundamentals and Applications
Издательство Prentice-Hall, 1983, -624 pp.

This book owes its beginnings to the pioneering work of Claude Shannon in 1948 on achieving reliable communication over a noisy transmission channel. Shannon's central theme was that if the signaling rate of the system is less than the channel capacity, reliable communication can be achieved if one chooses proper encoding and decoding techniques. The design of good codes and of efficient decoding methods, initiated by Hamming, Slepian, and others in the early 1950s, has occupied the energies of many researchers since then. Much of this work is highly mathematical in nature, and requires an extensive background in mode algebra and probability theory to understand. This has acted as an impediment to many practicing engineers and computer scientists, who are interested in applying these techniques to real systems. One of the purposes of this book is to present the essentials of this highly complex material in such a manner that it can be understood and applied with only a minimum of mathematical background.
Work on coding in the 1950s and 1960s was devoted primarily to developing the theory of efficient encoders and decoders. In 1970, the first author published a book entitled An Introduction to Error-Correcting Codes, which presented the fundamentals of the previous two decades of work covering both block and convolutional codes. The approach was to explain the material in an easily understood manner, with a minimum of mathematical rigor. The present book takes the same approach to covering the fundamentals of coding. However, the entire manuscript has been rewritten and much new material has been added. In particular, during the 1970s the emphasis in coding research shifted from theory to practical applications. Consequently, three completely new chapters on the applications of coding to digital transmission and storage systems have been added. Other major additions include a comprehensive treatment of the error-detecting capabilities of block codes, and an emphasis on probabilistic decoding methods for convolutional codes. A brief description of each chapter follows.

Coding for Reliable Digital Transmission and Storage.
Introduction to Algebra.
Linear Block Codes.
Cyclic Codes.
Error-Trapping Decoding for Cyclic Codes.
BCH Codes.
Majority-Logic Decoding for Cyclic Codes.
Finite Geometry Codes.
Burst -Error-Correcting Codes.
Convolutional Codes.
Maximum Likelihood Decoding of Convolutional Codes.
Sequential Decoding of Convolutional Codes.
Majority-Logic Decoding of Convolutional Codes.
Burst-Error-Correcting Convolutional Codes.
Automatic-Repeat-Request Strategies.
Appucations of Slock Codes for Error Control in Data Storage Systems.
Practical Appucations of Convolutional Codes.
A Tables of Galois Fields.
B Minimal Polynomials of Elements in GF(2m).
C Generator Polynomials of Sinary Primitive BCH Codes of Length up to 210-1.
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