Introduction to Coding and Information Theory
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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 cod...
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. TOC:Introduction:Preliminaries; Miscellany; Some Probability; Matrices1. An Introduction to CodesStrings and Things; What are codes? Uniquely Decipherable Codes;Instantaneous Codes and Kraft's Theorem2. Efficient EncodingInformation Sources; Average Codeword Length; Huffman Encoding; TheProof that Huffman Encoding is the Most Efficient3. Noiseless CodingEntropy; Properties of Entropy; Extensions of an Information 1= Source; The Noiseless Coding TheoremII Coding Theory4. The Main Coding Theory ProblemCommunications Channels; Decision Rules; Nearest Neighbor Decoding;
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