Introduction to Coding and
Information Theory
Introduction to Coding and
Information Theory
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. In addition, all of the needed elementary discrete probability is developed in a preliminary chapter. After a prelinimary chapter, there follows as 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 communications 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 Zp. The penultimate chapter is devoted to a study of the Hamming, Golay and Reed-Muller families of codes, along with some decimal codes and finally some codes obtained from Latin squares. The final chapter is a brief introduction to cyclic codes. It is the author's hope that this book will promote the teaching of elementary coding theory to undergraduates. We can think of no more elegant use of elementary linear probability than in elementary information theory and no more elegant use of elementary linear algebra than in elementary coding theory.
1997, ISBN 0-387-94704-3, 323 pp., Hardcover