Overview

Modern digital communication systems often require error-free transmission. For example, the information transmitted and received over a banking network must not contain errors. The issue of data integrity is becoming increasingly important, and there are many more situations where error protection is required.

In 1948, the fundamental concepts and mathematical theory of information transmission were laid by C. E. Shannon [1]. Shannon perceived that it is possible to transmit digital information over a noisy channel with an arbitrarily small error probability by proper channel encoding and decoding. The goal of approaching such error-free transmission can be achieved when the information transmission rate is less than the channel capacity, C _c, in bits per second. Since Shannon's work, a great deal of effort has been spent by many researchers to find good codes and efficient decoding methods for error-control. As a result, many different types of codes, namely block codes and convolutional codes, have been found and used in modern digital communication systems. This book is mainly concerned with the structures of binary and nonbinary, linear block codes, and the decoding techniques. The treatment here concentrates on the basic encoding and decoding principles of those block codes.

1.1 Introduction

The development of channel coding was motivated primarily by users who wanted reliable transmission in a communication system. This chapter describes the elements that make up a reliable communication system, then examines various types of transmission channels. The mathematical models presented here give an adequate description...