Chapter 1
Introduction to Digital and Analog
Communication Systems
(Sections 1 – 9)
Communication Model
Signal
Processing
Source
Computer
Telephone
Human
Camera
Server
Communication
(Transmitting)
Transmitter
Modem
Laser
Microwave
Transmitter
Microphone
Communication
(Receiving)
Channel
Wire
Air
Optical fiber
Water
Signal
Processing
Receiver
Modem
Photodetector
Microwave Dish
Microphone
Radio
Destination
Computer
Human
Speaker
Video screen
Server
Definition: A communication system is a system which
transmits information from a source to a destination.
Goals of ESE 471
• Understand how communication systems
work.
• Develop mathematical models for methods
and components of communication systems.
• Analyze performance of communication
systems and methods.
• Understand practical systems in use.
Definitions
• A digital information source produces a finite set of
possible messages
• An analog information source produces messages that are
defined on a continuum.
• A digital communication system transfers information from
a digital source to the intended receiver.
• An analog communication system transfers information
from an analog source to the intended receiver.
• A signal is a measurable quantity (e.g., voltage) which
bears information.
• Noise is a measurable quantity which carries undesired
interference.
Why Digital?
•
•
•
•
•
Less expensive circuits
Privacy and security
Small signals (less power)
Converged multimedia
Error correction and reduction
Why Not Digital?
• More bandwidth
• Synchronization in electrical circuits
• Approximated information
Realistic Communication Model
Noise and errors make communication inaccurate.
~ (t )  m (t ) , or make them as close as possible.
The goal is to achieve m
m(t) is the original signal at baseband.
s(t) is called the transmitted signal at carrier frequency.
Couch, Digital and Analog Communication Systems, Seventh Edition
©2007 Pearson Education, Inc. All rights reserved. 0-13-142492-0
Wireless
Frequency
Allocations in
the U.S.A.
Modes of Wireless
Wave Propagation
Information
• Electronic communication systems are
inherently analog.
• The process of communication is inherently
discrete.
• Limitations
– Noise or uncertainty
– Changes in system characteristics
Measure of Information
•
The amount of information sent from a digital source when the jth message is
transmitted is given by:
1
I j  log 2 
P
 j

 bits


where Pj is the probability of transmitting the jth message. (0  Pj  1, Ij  0)
•
Average information measure of a digital source is given by:
m
m
1
H   Pj I j   Pj log 2 
P
j 1
j 1
 j

 bits


where m is the number of possible different source messages. H is called the
entropy. H is maximum when all messages are equally likely.
• The redundancy of a source is H / Hmax.
e.g., parity bit adds redundancy to source with 8 bit
output.
• Deterministic signal processing never creates
information.
• If the source generates independent messages once
every T seconds, then the source rate R is:
H
R
bits / second
T
R can be viewed as the average information per
second.
Example 1-1
Digital words consisting of 12 digits and each digits can be
one of 4 equally likely possibilities.
12
Each word, j, has probability of occurrence, Pj:
Then:




 1 
I j  log 2 
bits  24 bits
12 
  1  
 4 
  
12
1
H   
j 1  4 
m
24  24 bits
1 1
Pj  12   
4
4
Another Example: 2 Dice
Suppose we are throwing 2 dice simultaneously and sum the two numbers. The
outcome, x, can be 2  x  12.
The possible scenarios for these outcomes are:
x = 2: (1, 1)
x = 3: (1, 2), (2, 1)
x = 4: (1, 3), (2, 2), (3, 1)
x = 5: (1, 4), (2, 3), (3, 2), (4, 1)
x = 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
x = 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
x = 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
x = 9: (3, 6), (4, 5), (5, 4), (6, 3)
x = 10: (4, 6), (5, 5), (6, 4)
x = 11: (5, 6), (6, 5)
x = 12: (6, 6)
Pr (x =2) = 1/36
Pr (x =3) = 2/36
Pr (x =4) = 3/36
Pr (x =5) = 4/36
Pr (x =6) = 5/36
Pr (x =7) = 6/36
Pr (x =8) = 5/36
Pr (x =9) = 4/36
Pr (x =10) = 3/36
Pr (x =11) = 2/36
Pr (x =12) = 1/36




1 

I 2  log 2
 log 2 36   3.58 bits
 1 
 
  36  




1 

I 3  log 2
 log 2 18  2.89 bits
 2 
 
  36  




1 

I 4  log 2
 log 2 12   2.48 bits
 3 
 
  36  




1 

I 5  log 2
 log 2 9   2.20 bits
 4 
 
  36  




1 

I 6  log 2
 log 2 7.2   1.97 bits
 5 
 
  36  




1 

I 7  log 2
 log 2 6   1.79 bits
 6 
 
  36  




1 

I 8  log 2
 log 2 7.2   1.97 bits
 5 
 
  36  




1 

I 9  log 2
 log 2 9   2.20 bits
 4 
 
  36  




1 

I10  log 2
 log 2 12   2.48 bits
 3 
 
  36  




1 

I11  log 2
 log 2 18  2.89 bits
 2 
 
  36  




1 

I12  log 2
 log 2 36   3.58 bits
 1 
 
  36  
 1 
 2 
 3 
 4 
 5 
 6 
 5 
H 
 3.58  
 2.89   
 2.48  
 2.20   
 1.97   
 1.79   
 1.97 
 36 
 36 
 36 
 36 
 36 
 36 
 36 
 4 
 3 
 2 
 1 

 2.20   
 2.48  
 2.89   
 3.58
 36 
 36 
 36 
 36 
H  2.27 bits
Dice Example Continued
•
•
H = 2.27 bits implies that in order to communicate the outcome of throwing two
dice, it requires a minimum of 2.27 bits. How can we achieve this?
For example, when we get a certain x, send a binary sequence corresponding to
it as shown below.
x = 2: 11010 
x = 3: 11011 
x = 4: 1100 
x = 5: 000

x = 6: 001

x = 7: 10

x = 8: 010 
x = 9: 011

x = 10: 1110 
x = 11: 11110 
x = 12: 11111 
5 bits with Pr (x =2) = 1/36
5 bits with Pr (x =3) = 2/36
4 bits with Pr (x =4) = 3/36
3 bits with Pr (x =5) = 4/36
3 bits with Pr (x =6) = 5/36
2 bits with Pr (x =7) = 6/36
3 bits with Pr (x =8) = 5/36
3 bits with Pr (x =9) = 4/36
4 bits with Pr (x =10) = 3/36
5 bits with Pr (x =11) = 2/36
5 bits with Pr (x =12) = 1/36
Average bits needed per message = 3.33 bits. Can you think of any other scheme?
Channel Capacity
In 1948, Claude Shannon developed a mathematical model for
channel such that, insofar as the model is realistic, there exists
an upper limit on the rate at which information can be
transmitted from source to user error-free. This upper limit is
called the channel capacity, C. It is a function of bandwidth
(B) and signal-to-noise ration (S/N or SNR).
S

C  B log 2 1  
 N
Coding
Coding Theory is the study of preprocessing
the source information such that the channel
capacity can be achieved (or get as close to it
as possible).
coding