Introduction to coding and information theory / Steven Roman.

Format:

Book

Author/Creator:

Roman, Steven

Series:

Undergraduate texts in mathematics

Language:

English

Subjects (All):

Coding theory.

Information theory.

Physical Description:

xiii, 323 pages : illustrations ; 25 cm.

Place of Publication:

New York : Springer, [1997]

Summary:

This book is an introduction to coding and information theory, with an emphasis on coding theory. It is suitable for undergraduates with a modest mathematical background. While some previous knowledge of elementary linear algebra is helpful, it is not essential. All of the needed elementary discrete probability is developed in a preliminary chapter. After a preliminary chapter, there follows an introductory chapter on variable-length codes that culminates in Kraft's Theorem. Two chapters on Information Theory follow - the first on Huffman encoding and the second on the concept of the entropy of an information source, culminating in a discussion of Shannon's Noiseless Coding Theorem. The remaining four chapters cover the theory of error-correcting block codes. The first chapter covers communication channels, decision rules, nearest neighbor decoding, perfect codes, the main coding theory problem, the sphere-packing, Singleton and Plotkin bounds, and a brief discussion of the Noisy Coding Theorem. There follows a chapter on linear codes that begins with a discussion of vector spaces over the field (actual symbol not reproducible). The penultimate chapter is devoted to a study of the Hamming, Golay, and Reed-Muller families of codes, along with some decimal codes and some codes obtained from Latin squares. The final chapter contains a brief introduction to cyclic codes.

Notes:

Includes bibliographical references (pages 317-318) and index.

ISBN:

0387947043

OCLC:

34355037