Introduction to Coding and Information Theory (Undergraduate Texts in Mathematics) - Hardcover

Roman, Steven

Hardcover

ISBN 10: 0387947043 ISBN 13: 9780387947044

Verlag: Springer, 1996

Inhaltsangabe

This book is intended to introduce coding theory and information theory to undergraduate students of mathematics and computer science. It begins with a review of probablity theory as applied to finite sample spaces and a general introduction to the nature and types of codes. The two subsequent chapters discuss information theory: efficiency of codes, the entropy of information sources, and Shannon's Noiseless Coding Theorem. The remaining three chapters deal with coding theory: communication channels, decoding in the presence of errors, the general theory of linear codes, and such specific codes as Hamming codes, the simplex codes, and many others.

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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 1996
• Sprache: Englisch
• ISBN 10: 0387947043
• ISBN 13: 9780387947044
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 340
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland