Research Catalog

Details

Description

1. xiii, 323 pages : illustrations; 24 cm.

Summary

1. "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."--BOOK JACKET.

Series statement

1. Undergraduate texts in mathematics

Uniform title

1. Undergraduate texts in mathematics.

Subject

1. Coding theory
2. Information theory

Contents

1. 0. Preliminaries -- 1. An Introduction to Codes -- 2. Efficient Encoding -- 3. Noiseless Coding -- 4. The Main Coding Theory Problem -- 5. Linear Codes -- 6. Some Special Codes -- 7. An Introduction to Cyclic Codes.

Owning institution

1. Columbia University Libraries

Bibliography (note)

1. Includes bibliographical references (p. 317-318) and index.