Togneri / deSilva Fundamentals of Information Theory and Coding Design

1. Auflage 2006
ISBN: 978-1-135-44185-2
Verlag: CRC Press
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 385 Seiten

Reihe: Discrete Mathematics and Its Applications

Books on information theory and coding have proliferated over the last few years, but few succeed in covering the fundamentals without losing students in mathematical abstraction. Even fewer build the essential theoretical framework when presenting algorithms and implementation details of modern coding systems.

Without abandoning the theoretical foundations, Fundamentals of Information Theory and Coding Design presents working algorithms and implementations that can be used to design and create real systems. The emphasis is on the underlying concepts governing information theory and the mathematical basis for modern coding systems, but the authors also provide the practical details of important codes like Reed-Solomon, BCH, and Turbo codes. Also setting this text apart are discussions on the cascading of information channels and the additivity of information, the details of arithmetic coding, and the connection between coding of extensions and Markov modelling.

Complete, balanced coverage, an outstanding format, and a wealth of examples and exercises make this an outstanding text for upper-level students in computer science, mathematics, and engineering and a valuable reference for telecommunications engineers and coding theory researchers.

Zielgruppe

Undergraduate students in information theory and communications; Graduate students and professionals in information technology; Applied mathematicians in discrete mathematics, combinatorics, and coding theory

Autoren/Hrsg.

Togneri, Roberto

deSilva, Christopher J.S

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik EDV | Informatik Technische Informatik Computersicherheit

Inhaltsverzeichnis

ENTROPY AND INFORMATION

Structure
Structure in Randomness
First Concepts of Probability Theory

Surprise and Entropy
Units of Entropy
The Minimum and Maximum Values of Entropy

A Useful Inequality

Joint Probability Distribution Functions
Conditional Probability and Bayes' Theorem

Conditional Probability Distributions and Conditional Entropy
Information Sources
Memoryless Information Sources

Markov Sources and n-Gram Models
Stationary Distributions
The Entropy of Markov Sources
Sequences of Symbols

The Adjoint Source of a Markov Source
Extensions of Sources

Infinite Sample Spaces

INFORMATION CHANNELS

What Are Information Channels?

BSC and BEC Channels
Mutual Information

Noiseless and Deterministic Channels

Cascaded Channels

Additivity of Mutual Information

Channel Capacity: Maximum Mutual Information
Continuous Channels and Gaussian Channels

Information Capacity Theorem

Rate Distortion Theory

SOURCE CODING

Introduction

Instantaneous Codes
The Kraft Inequality and McMillan's Theorem
Average Length and Compact Codes
Shannon's Noiseless Coding Theorem

Fano Coding
Huffman Coding
Arithmetic Coding

Higher-Order Modelling
DATA COMPRESSION

Introduction

Basic Concepts of Data Compression

Run-Length Coding

The CCITT Standard for Facsimile Transmission

Block-sorting Compression
Dictionary Coding

Statistical Compression
Prediction by Partial Matching

Image Coding
FUNDAMENTALS OF CHANNEL CODING

Introduction

Code Rate
Decoding Rules

Hamming Distance

Bounds on M, Maximal Codes and Perfect Codes
Error Probabilities

Shannon's Fundamental Coding Theorem

ERROR-CORRECTING CODES

Introduction

Groups

Rings and Fields
Linear Spaces
Linear Spaces over the Binary Field
Linear Codes
Encoding and Decoding
Codes Derived from Hadamard Matrices

CYCLIC CODES

Introduction

Rings of Polynomials
Cyclic Codes
Encoding and Decoding of Cyclic Codes

Encoding and Decoding Circuits for Cyclic Codes
The Golay Code
Hamming Codes
Cyclic Redundancy Check Codes

Reed-Muller Codes

BURST-CORRECTING CODES

Introduction

Finite Fields
Irreducible Polynomials
Construction of Finite Fields
Bursts of Errors

Fire Codes

Minimum Polynomials

Bose-Chaudhuri-Hocquenghem Codes
Other Fields
Reed-Solomon Codes

CONVOLUTIONAL CODES

Introduction

ASimple Example

Binary Convolutional Codes
Decoding Convolutional Codes
The Viterbi Algorithm

Sequential Decoding
Trellis Modulation

Turbo Codes
INDEX

Each chapter also contains a section of exercises and a section of references.