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6.450 Principles of Digital Communications Wednesday, Sept. 4

MIT, Fall 2002 Handout #3

Lecture 1: Introduction to Digital Communication

1 Introduction and Objectives

The digital communication industry is an enormous and rapidly growing industry, roughly

comparable in size to the computer industry. The objective of this course is to study those

aspects of digital communication systems that are unique to these systems. That is, rather

than focusing on hardware and software for these systems, which is much like hardware

and software for many other kinds of systems, we focus on the fundamental system aspects

of modern digital communication.

This is the ﬁrst subject in the two-term sequence, 6.450 and 6.451. The two subjects are

in the process of being integrated into a coherent year-long sequence, and we hope that

the rough edges do not show too much. Our intention is that 6.450 may be taken on a

stand-alone basis and be accessible to well-prepared undergraduates.

Digital communication is a ﬁeld in which theoretical ideas have had an unusually pow-

erful impact on actual system design. The basis of the theory was developed 53 years

ago by Claude Shannon, and is called information theory. For the ﬁrst 25 years or so of

its existence, information theory served as a rich source of academic research problems

and as a tantalizing suggestion that communication systems could be made more eﬃcient

and more reliable by using these approaches. By the mid 1970’s, mainstream systems

using information theoretic ideas began to be widely implemented, for two reasons. First,

by that time there were a sizable number of engineers who understood both information

theory and communication system development. Second, the low cost and increasing pro-

cessing power of digital hardware made it possible to implement increasingly sophisticated

algorithms.

As you learn about digital communication systems and their conceptual basis in infor-

mation theory, you will come to appreciate that these ideas require a fairly deep under-

standing of somewhat abstract concepts. Doing the problem sets is an important part

of developing this understanding, but it is not suﬃcient. In many undergraduate engi-

neering subjects, the emphasis (reinforced by the grading policy) is on learning to grind

through the solution of a set of types of problems represented by prescribed equations

(“plug and chug”). Here, as is appropriate for a graduate class, the focus is much more

on the connections between engineering and theory.

The relationship between theory, problem sets, and engineering/design is rather complex.

The theory deals with relationships and analysis for models of real systems. A good

theory (and information theory is one of the best) allows for simple analysis of simpliﬁed

models. It also provides structural principles that allow insights from these simple models

to be applied to more complex and realistic models. Problem sets provide students with

an opportunity to analyze these highly simpliﬁed models, and, with patience, to start to

understand the general principles. Engineering deals with making the approximations and

judgment calls to create appropriate simple models, and from there to design workable

systems.

The important point here is that engineering (at this level) cannot really be separated

from theory. Engineering is necessary to theory in choosing appropriate models, and

theory is necessary to engineering to create principles and quantitative results. Engineer-

ing sometimes becomes overly concerned with detail, and theory overly concerned with

mathematical niceties, but we shall try to avoid both these excesses here.

We urge you, when you ﬁnish an exercise, to spend some time thinking about what it

means, how the solution technique might be extended to more general problems, whether

the model used in the exercise makes much sense physically, etc. We will try to encourage

this both by keeping the number of exercises limited and by making it necessary to achieve

this deeper understanding about one exercise in order to do the next.

In terms of depth, this subject is more like a graduate subject than undergraduate. How-

ever, it requires only a knowledge of elementary probability (6.041) and linear systems

(6.003), so it can be understood at the undergraduate level. Learning to think more

deeply about the material, in addition to solving the exercises, will be invaluable both in

the workplace and in graduate work.

This is an experimental subject, both in terms of content and approach. Some undergrad-

uate courses aim to make the student familiar with a large variety of diﬀerent systems that

have been implemented historically. In our opinion such an approach does not help much

in understanding the new systems being designed currently, and provides little insight

into the diﬀerent design choices that might be made. Our objective here is to develop

the relatively small number of underlying principles guiding all of these systems, with the

hope that you can then understand the details of any system of interest on your own.

We need your help in this experiment. Let us know, by direct comment or by e-mail,

what interests you, what turns you oﬀ, what is too hard, what seems too easy, etc. We

think we know what you should learn, but are less certain about how to help you learn it.

2 Networks and Layering

The communication systems that you use every day— e.g., the telephone system, the

Internet— are networks of incredible complexity, made up of an enormous variety of

equipment made by diﬀerent manufacturers at diﬀerent times following diﬀerent design

principles. Such complex networks need to be based on some simple architectural princi-

ples in order to be understood, managed and maintained.

Two fundamental architectural principles of communication networks are standardized

interfaces and layering.

A standardized interface allows the user or equipment on one side of the interface to ignore

all details about the other side of the interface except for certain speciﬁed characteristics.

For example, the standard interface in the telephony system for decades has been the 4

KHz voice channel. You can plug a telephone into a wall plug anywhere in the world

(subject to further electrical, mechanical and dialing interface standards), and expect to

be able to send a nominal 4 KHz voice signal anywhere in the Public Switched Telephone

Network (PSTN). Other standardized interfaces are deﬁned at various levels within the

telephone network.

The trend in recent decades has been to make all standardized interfaces digital, at least

inside the telephone and other networks, and increasingly at the user interface as well. Ba-

sically, one sends and receives bits, regardless of the ultimate application. Thus electronic

communication is becoming synonymous with digital communication.

The idea of layering in communication networks is to break up communication functions

into separable modules, or “layers,” which (a) communicate with higher and lower layers

via standardized interfaces, and (b) communicate through networks (via lower layers) to

counterpart modules (“peer layers”) elsewhere in the network. Often peer modules occur

in pairs, each containing both transmit and receive functions.

For example, a modem (modulator-demodulator) (a) receives a sequence of bits from a

higher-level application or user; (b) generates from the received data a modulated signal

for transmission through a standardized interface over a channel; (c) receives from the

channel a signal that is a more-or-less faithful replica of a signal transmitted by a remote

modem; and (d) generates from the received signal a demodulated bit sequence that is

supposed to be a more-or-less faithful replica of the bit sequence that entered the remote

modem.

Other examples of paired modules at the same layer are: telephones; encryp-

tor/decryptors; speech encoder/decoders; image encoder/decoders; error-correction en-

coder/decoders; etc.

In more complicated situations, there may be more than two paired elements in a layer.

For example, in a wireless system each receiver may be listening to many transmitters.

The multi-access control issues that arise in such cases are beyond the scope of this

course; diﬀerent aspects of these issues are addressed in, e.g., 6.451 (Principles of Digital

Communication II), 6.263 (Data Networks), and 6.441 (Information Theory).

3 Block Diagram of a Generic Point-to-Point Digital

Communication System

This course focuses on two fundamental problems of data communication: source coding

and channel coding.

The source coding problem is the problem of eﬃcient representation of source signals—

e.g., speech waveforms, image waveforms, text ﬁles— as a sequence of bits for transmission

through a digital network. Of course we must keep in mind the paired problem of source

decoding: conversion of the bit sequence (possibly corrupted) back into a more-or-less

faithful replica of the original source signal.

The channel coding problem is the problem of eﬃcient transmission of a sequence of bits

through a lower-layer channel— e.g., a 4 KHz telephone channel or a wireless channel.

Again we must very much keep in mind how we intend to recover a more-or-less faithful

replica of the original bit sequence from the channel output in the remote receiver, despite

the distortions that may be introduced by the channel.

In a simple point-to-point channel, illustrated below in the classic “Figure 1” of every

information theory text, these are the only two layers. The output bit sequence of the

source encoder is the input bit sequence of the channel encoder, and the output bit

sequence of the channel decoder is the input bit sequence of the source decoder.

Input

Source

Encoder

Channel

Encoder

Channel



Source

Decoder



Channel

Decoder



Output

“Figure 1.” Separation of source and channel coding.

The astute student may ask at this point whether anything is lost by separate source and

channel coding as shown in “Figure 1.” Could joint source-channel coding achieve better

performance or reduced complexity?

One of the remarkable basic theorems of information theory is that, in a sense, nothing

is lost in terms of performance. If a source signal can be communicated through a given

point-to-point channel within some level of distortion by any means whatsoever, then

separate source and channel coding can also be designed to stay within that same level

of distortion. We will give some insight into this source-channel coding separation

theorem during this course; 6.441 (Information Theory) explains it more fully.

The source-channel coding separation theorem does not rule out the possibility of smaller

delay or lower complexity using joint source-channel coding. Also, there are more complex

network scenarios in which this theorem does not hold.

However, the advantages of standardized binary interfaces and of layering, discussed in the

previous section, are so overwhelming that joint source-channel coding is rarely attempted

in practice.

3.1 Input

We now discuss the various elements of “Figure 1” in more detail.

The input is the source signal. It might be a sequence of symbols such as letters from

the English or Chinese alphabet, binary symbols from a computer ﬁle, etc. Alternatively,

the input might be a waveform, such as a voice signal from a microphone, the output of

a sensor, a video waveform, etc. Or, it might be a sequence of images such as X-rays,

photographs, etc.

Whatever the source signal is, we will model it as a sample function of a random process.

This is one of the reasons why probability is an essential prerequisite for this subject. It

is not obvious why inputs to communication systems should be modeled as random, and

in fact this was not appreciated before Shannon developed information theory in 1948.

The study of communication before that time (and well after that time) was based on

Fourier analysis, which basically studies the eﬀect of passing sine waves through various

kinds of systems and components. We will start our study of channels with this kind of

analysis (often called Nyquist theory in the context of digital communication) to develop

basic results about sampling, intersymbol interference, and bandwidth.

However, Shannon’s view was that if the recipient knows that a sine wave of a given

frequency is to be communicated, why not simply regenerate it at the output rather than

send it over a long distance? Or, if the recipient knows that a sine wave of unknown

frequency is to be communicated, why not simply send the frequency rather than the

entire waveform?

The essence of Shannon’s viewpoint is that we should focus on the set of possible inputs

from the source rather than any particular input. The objective then is to transform each

possible input into a transmitted signal in such a way that each possible transmitted signal

can be distinguished from the others at the output. A probability measure is needed on

this set of possible inputs to distinguish typical inputs from abnormal inputs. We shall

see in the rest of this subject how this point of view drives the processing of the inputs

as they pass through a communication system.

3.2 Source Coding

The source encoder in “Figure 1” has the function of converting the input from its original

form into a sequence of bits. We have already discussed many of the reasons for conver-

sion to a bit sequence: standardized interfaces, layering, and the source-channel coding

separation theorem.

The simplest source coding techniques involve simply representing the source signal by

a sequence of symbols from some ﬁnite alphabet, and then coding the alphabet symbols

into ﬁxed-length blocks of bits. For example, letters from the 27-symbol English alphabet

(including a space symbol) may be encoded into 5-bit blocks. Or, upper-case letters,

lower-case letters, and a great many other special symbols may be converted into 8-bit

blocks (“bytes”) using the standard ASCII code.

The most straightforward approach to converting an analog waveform to a bit sequence,

called analog to digital (A/D) conversion, is ﬁrst to sample the source at a suﬃciently high

rate (called the “Nyquist rate”), and then to quantize it suﬃciently ﬁnely for adequate

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skyknight2009

2013-06-21

在数字通信领域，MIT的讲义可算个经典了。

Principle of Digital Communication I_MIT数字通信原理讲义

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