Introduction to Coding and Information Theory

This book is an introduction to coding theory and information theory for undergraduate students of mathematics and computer science. Among the topics it discusses are: a review of probablity theory; the efficiency of codes, the capacity of communications channels, coding and decoding in the presence of errors, the general theory of linear codes, and examples of specific codes used in ordinalry communications as wwell as cryptography.

Autorentext

Steven Roman is Professor Emeritus of Mathematics at California State University Fullerton. He is the author of numerous other mathematics textbooks, including Field Theory (2006), Advanced Linear Algebra (2008), Fundamentals of Group Theory (2012), Introduction to the Mathematics of Finance (2012), and An Introduction to Catalan Numbers (2015).

Inhalt
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;