Coding and Information Theory, 2 edition
| Date: 12 April 2011, 11:27
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Preface to the First Edition
This book combines the fields of coding and information theory in a natural way. They are both theories about the representation of abstract
symbols. The two fields are now each so vast that only the elements can be presented in a short book.
Information theory is usually thought of as "sending information from here to there" (transmission of information), but this is exactly the same as "sending information from now to then" (storage of information). Both situations occur constantly when handling information.
Clearly, the encoding of information for efficient storage as well as reliable recovery in the presence of "noise" is essential in computer science.
Since the representation, transmission, and transformation of information are fundamental to many other fields as well as to computer science, it is time to make the theories easily available. Whenever and wherever problems of generation, storage, or processing of information arise, there is a need to know both how to compress the textual naaterial as well as how to protect it against possible mutilation. Of the many known encoding methods, we can indicate only a few of the more important ones, but hopefully the many examples in the text will alert the student to other possibilities.
The text covers the fundamentals of the two fields and gives examples of the use of the ideas in practice. The amount of background mathematics and electrical engineering is kept to a minimum. The book uses, at most, simple calculus plus a little probability theory, and anything beyond that is developed as needed. Techniques that have recently arisen in computer science are used to simplify the presentation and the proofs of many results. These techniques are explained where they are used, so no special knowledge of computer science is required.
Many other proofs have been greatly simplified, and when necessary new material has been developed to meet current technological needs.
An effort has been made to arrange the material, especially the proof of Shannon's main result, so that it is evident why the theorems are true, not just that they have been proved mathematically.
Chapter 11, on algebraic codes, develops the needed mathematics of finite fields. Because of its mathematical difficulty, this chapter is placed last and out of logical order. It can follow Chapter 3, if desired. There is a deliberate repetition in the text; important ideas are usually presented at least twice to ensure that the reader understands them. The text leaves out large areas of knowledge in the belief that it is better to master a little than to half know a lot. Thus more material may easily be added (at the discretion of the teacher) when it seems appropriate for the class.
I have folloffed custom in referring to Hamming codes and Hamming distance; to do otherwise would mislead the student and be false modesty.
R. W. HAMMING
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