Clark G.C., Cain J.B. Error-Correction Coding for Digital Communications

Springer, 1981. — 432 p.Error-correction coding is being used on an almost routine basis in most new communication systems. Not only is coding equipment being used to increase the energy efficiency of communication links, but coding ideas are also providing innovative solutions to many related communication problems. Among these are the elimination of intersymbol interference caused by filtering and multipath and the improved demodulation of certain frequency modulated signals by taking advantage of the "natural" coding provided by a continuous phase. Although several books and numerous articles have been written on coding theory, there are still noticeable deficiencies. First, the practical aspects of translating a specific decoding algorithm into actual hardware have been largely ignored. The information that is available is sketchy and is widely dispersed. Second, the information required to evaluate a particular technique under situations that are encountered in practice is available for the most part only in private company reports.
This book is aimed at correcting both of these problems. It is written for the design engineer who must build the coding and decoding equipment and for the communication system engineer who must incorporate this equipment into a system. It is also suitable as a senior-level or first-year graduate text for an introductory one-semester course in coding theory.
The book uses a minimum of mathematics and entirely avoids the classical theorem/proof approach that is often seen in coding texts. Whenever possible heuristic arguments are advanced and concepts are developed by drawing analogies. We have intentionally constrained the level of mathematical rigor used in presenting error-correction concepts. Notwithstanding, coding is an extremely mathematical subject, and it would be an impossible task to attempt to present the material with no mathematics at all. The assumption is made that the practicing engineer is mostly interested in using the mathematics and not in constructing rigorous proofs. Thus, the goal is to develop a manipulative and intuitive understanding through numerous examples. Although there are many perils in this approach, a capable engineer can usually verify that a particular procedure is correct by trying it on a few test cases. The serious student may later wish to round out his or her understanding by pursuing the subject to its very roots. In addition to the large number of papers in the open literature. the excellent texts by Peterson and Weldon, Berlekamp and Gallager are highly recommended for this purpose.
Not all aspects of coding theory are treated in equal depth. Some topics, such as coding bounds, are treated very lightly while some others, such as certain classes of rarely used codes, are omitted entirely. Numerous classes of codes of practical interest are discussed in terms of methods of construction and code properties. However. there exist additional interesting properties of these codes as well as other code classes which we have chosen to omit for reasons of brevity. Instead, we have chosen to emphasize the formulation and implementation of decoding algorithms. The viewpoint, the selection of topics, and the degree of emphasis largely reflects the authors' personal preference and is based upon 15 years of practical experience in designing and evaluating coding equipment. However, we feel that the approach we have taken will also provide the reader with the insight and motivation to undertake some of the more difficult topics in other texts.
In this book the application of error-correction coding is presented in the context of communication system design. Again, this reflects the authors' personal preferences. These techniques may also be used in other applications such as in computer memory systems. We have attempted to develop the tools necessary to enable the reader to evaluate such applications and to select an appropriate coding/decoding technique.Fundamental Concepts of Coding
Group Codes
Simple Nonalgebraic Decoding Techniques for Group Codes
Soft Decision Decoding of Block Codes
Algebraic Techniques for Multiple Error Correction
Convolutional Code Structure and Viterbi Decoding
Other Convolutional Decoding Techniques
System Applications
A. Code Generators for BCH Codes
B. Code Generators for Convolutional Codes