Introduction to Coding and Information Theory / Edition 1

by Steven Roman

Overview

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.

Product Details

ISBN-13:	9780387947044
Publisher:	Springer New York
Publication date:	11/26/1996
Series:	Undergraduate Texts in Mathematics
Edition description:	1997
Pages:	326
Product dimensions:	7.01(w) x 10.00(h) x 0.03(d)

Table of Contents

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;