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.
Introduction: Preliminaries; Miscellany; Some Probability; Matrices 1. An Introduction to Codes Strings and Things; What are codes? Uniquely Decipherable Codes; Instantaneous Codes and Kraft's Theorem 2. Efficient Encoding Information Sources; Average Codeword Length; Huffman Encoding; The Proof that Huffman Encoding is the Most Efficient 3. Noiseless Coding Entropy; Properties of Entropy; Extensions of an Information 1= Source; The Noiseless Coding Theorem II Coding Theory 4. The Main Coding Theory Problem Communications Channels; Decision Rules; Nearest Neighbor Decoding;
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