Wiley Encyclopedia of Telecommunications Vol II.pdf

WILEY ENCYCLOPEDIA OF

TELECOMMUNICATIONS

VOLUME 2

WILEY ENCYCLOPEDIA OF TELECOMMUNICATIONS

Editor

John G. Proakis

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University of California at San Diego

Gerd Keiser

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Allen Levesque

Consultant

Larry Milstein

University of California at San Diego

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Analog Devices

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WILEY ENCYCLOPEDIA OF

TELECOMMUNICATIONS

VOLUME 2

John G. Proakis

Editor

A John Wiley & Sons Publication

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Library of Congress Cataloging in Publication Data:

Wiley encyclopedia of telecommunications / John G. Proakis, editor.

p. cm.

includes index.

ISBN 0-471-36972-1

1. Telecommunication—Encyclopedias. I. Title: Encyclopedia of

telecommunications. II. Proakis, John G.

TK5102 .W55 2002

621.382 03—dc21

2002014432

Printed in the United States of America

10987654321

DATA COMPRESSION

(or approximately restored) by the source decoder. The

channel code achieves the goal of reliable transmission:

The channel encoder inserts a small amount of redundancy

in the channel input stream that will allow the channel

decoder to correct the transmission errors in that stream

that are caused by the channel.

2. Combined Code Design .Oneode(asinFig.1)

is designed to accomplish the twin goals of bandwidth

efﬁciency and reliable transmission. Clearly, combined

code design is more general than separated code design.

However, previously separated codes were preferred to

combined codes in data communication system design.

There were two good reason for this: (a) Claude Shannon

showed that if the data sequence is sufﬁciently long,

and if the probabilistic models for the source and the

channel are sufﬁciently simple, then there is no loss in the

bandwidth versus reliability tradeoff that is achievable

using separated codes of arbitrary complexity instead of

combined codes of arbitrary complexity; and (b) the code

design problem is made easier by separating it into the two

decoupled problems of source code design and channel code

design. For the communication of short data sequences, or

for the scenario in which the complexity of the code is to be

constrained, there can be an advantage to using combined

codes as opposed to separated codes; consequently, there

much attention has focused on the combined code design

problem since the mid-1980s. At the time of the writing of

this article, however, results on combined code design are

somewhat isolated and have not yet been combined into a

nice theory. On the other hand, the two separate theories

of source code design and channel code design are well

developed. The purpose of the present article is to provide

an introduction to source code design.

J OHN K IEFFER

University of Minnesota

Minneapolis, Minnesota

1. INTRODUCTION

A modern-day data communication system must be

capable of transmitting data of all types, such as text,

speech, audio, image or video data. The block diagram in

Fig. 1 depicts a data communication system, consisting of

source, encoder, channel ,and decoder :

The source generates the data sequence that is to

be transmitted through the data communication system.

The encoder converts the data sequence into a binary

codeword for transmission through the channel. The

decoder generates a reconstructed data sequence that

may or not be equal to the original data sequence.

The encoder/decoder pair in Fig. 1 is the code of the

data communication system. In Fig. 1, the source and

channel are ﬁxed; the choice of code is ﬂexible, in order

to accomplish the twin goals of bandwidth efﬁciency and

reliable transmission , described as follows:

1. Bandwidth efﬁciency —the portion of the available

channel bandwidth that is allocated in order

to communicate the given data sequence should

be economized.

2. Reliable transmission —the reconstructed data

sequence should be equal or sufﬁciently close to

the original data sequence.

Unfortunately, these are conﬂicting goals; less use of

bandwidth makes for less reliable transmission, and

conversely, more reliable transmission requires the use

of more bandwidth. It is the job of the data communication

system designer to select a code that will yield a good

tradeoff between these two goals. Code design is typically

done in one of the following two ways.

In source code design, one can assume that the

communication channel introduces no errors, because

the purpose of the channel code is to correct whatever

channel errors occur. Thus, we may use Fig. 3 below, which

contains no channel, as the conceptual model guiding

source code design.

The system in Fig. 3 is called a data compression

system —it consists of the source and the source code

consisting of the (source encoder, source decoder) pair.

The data sequence generated by the source is random

and is denoted X n ; the notation X n is a shorthand for the

following random sequence of length n :

1. Separated Code Design . Two codes are designed,

a source code and a channel code , and then the source

code and the channel code are cascaded together. Figure 2

illustrates the procedure. The source code is the pair

consisting of the source encoder and source decoder; the

channel code is the (channel encoder, channel decoder)

pair. The source code achieves the goal of bandwidth

efﬁciency: The source encoder removes a large amount of

redundancy from the data sequence that can be restored

X n

= (X 1 , X 2 ,...,X n )

( 1 )

The X i values (i = 1 , 2 ,...,n) are the individual data

samples generated by the source. In Fig. 3, B K

is a

Source

Data

Encoder

Binary

Channel

Decoder

Reconstructed

sequence

codeword

data sequence

Figure 1. Block diagram of data communication system.

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