Ii Communications Channel

COMMUNICATION CHANNELS
INTRODUCTION TO SIGNALS

F A cycle is the part of the signal that repeats itself. Not
all signals have cycles.

v

t

cycle

F Signals with cycles are called periodic signals while
signals which do not have cycles are called aperiodic
signals.

F The period (τ) of a periodic signal is the length of time
of its cycle.

Communications Channels 1

F The frequency (f) of a signal is the number of cycles
per unit time of the signal. Frequency is measured in
cycles per second or hertz (Hz).

Example:

If a cycle is 0.4 ms long, then its frequency is:

1 cycle
f= -3
= 2,500 cycles/second or Hz
0.4 x 10 sec

F The frequency of a signal is therefore the reciprocal of
its period. ( f = 1 / τ ).

Example:

If the period of signal is 6 µs long, then its
frequency is:

1 1
f= =
τ 6 x 10 - 6

= 166,666.67 Hz or 166.67 KHz


F The frequency of a signal can also be computed by:

f= v
λ

where:

v velocity of signal movement through the
channel in meters per second

λ wavelength or the length of one cycle in
meters

Example:

If the velocity of the signal is 250,000 km/sec and
its wavelength is 0.25 m, then its frequency is:

v 250,000 x 10 3
f= =
λ 0.25

= 1 x 109 Hz or 1 GHz


COMMUNICATION SYSTEMS

F A communication system is a group of hardware (and
possibly software) that can facilitate communication.

F Shannon Block Diagram of a Communication System:

Information
Transmitter Channel Receiver Destination
Source

modulation demodulation
encoding decoding
encryption decryption

Noise
Source

INFORMATION SOURCE

F The communication system exists to communicate a
message. This message comes from the information
source

F In electronic communication systems, what is
important is the quantity of the information being
transmitted, not the quality.


TRANSMITTER

F The message or information to be transmitted must be
electrical in nature.

F If it is not yet electrical, then it must be first converted
into electrical energy by using the appropriate
transducer. A transducer is a device that converts a
physical quantity such as force, pressure, sound, level,
and temperature into electrical energy.

Example:

A microphone is a transducer that converts sound
into electrical signals.

F Most information signals are in the audio (low
frequency) frequency range.

Examples:

Telephone Speech - 300 Hz to 3,400 Hz
Natural Speech - 80 Hz to 8,000 Hz
Good Quality Music - 50 Hz to 15,000 Hz

F Audio signals may be transmitted directly by wire.


F However, several difficulties are involved in the
transmission of audio signals by electromagnetic
waves or radio waves (transmission by air).

F For sufficient radiation and reception of audio signals,
the transmitting and receiving antennas should have
dimensions comparable to the wavelength of the signal
to be transmitted.

λ = v/f

All electromagnetic waves propagate at a velocity near
the speed of light.

v ≈ 300,000 km / s

Example:

Shortest wavelength of music:

λ = v/f

= 300,000 x 103 / 15 x 103

= 20,000 m

Therefore, to transmit music via electromagnetic
transmission, the transmitting and receiving
antennas should have dimensions comparable to
20 Km.


F The solution to this problem is to translate or change
the frequency of the audio signal to be transmitted to a
much higher value.

Example:

If f = 15 MHz

λ = v/f

= 300,000 x 103 / 15 x 106

= 20 m

F This process of translation is called modulation. In
the process of modulation, some characteristic of a
high-frequency sine wave (called the carrier) is varied
in accordance with the instantaneous value of the
information or message signal (called the modulating
signal).


F General equation of a sine wave:

v(t) = V sin (ωt + θ)
or
v(t) = V sin (2πft + θ)

where:

V = maximum amplitude

ω = angular velocity
= 2πf
frequency

θ = phase angle (with respect to some
reference)

v(t)

V
t
V

T = 1/f

period


F The three characteristics or parameters of a sine wave
are amplitude, frequency, and phase angle. Any of
these may be varied by the modulating signal, giving
rise to amplitude, frequency, and phase modulation.

carrier
signal

0 1 0 0 1 1
information
signal

amplitude
modulated
signal

frequency
modulated
signal

phase
modulated
signal

F A modulated signal is just simply the carrier in another
form.


F Another benefit from modulation:

If two of more radio stations were able to come
up with a 20 Km antenna, they can transmit
music without going through the process of
modulation.

However, since all music is concentrated within
the range from 20 Hz to 20 KHz, all signals
coming from the different stations would be
hopelessly and inseparably mixed up.

If each station has its own unique carrier and
modulation was used, then each message signal
(music) will be translated into different
frequencies thus enabling the receiver to separate
the transmission of one station from other
stations.

F Therefore, the two major reasons for needing
modulation are:

1. So that a relatively smaller antenna can be
used to transmit electromagnetic signals.

2. So that signals with similar frequencies can
be transmitted without interference from one
another.


CHANNEL

F The channel is the medium of transmission. It is the
physical or non-physical link between transmitter and
receiver.

Examples:

wire (copper)
coaxial cable physical
fiber optics

radio waves non-physical

F If the transmission channel used is electromagnetic
propagation, the frequency of the carrier used must be
specified.

Example:

DWRT - 99.5 MHz


F The channel is affected by two factors:

1. Attenuation. Attenuation is the heavily fading of
signals. The farther the signal goes away from
the transmitter, the weaker it gets.

2. Noise. Noise is any unwanted energy. Noise can
actually affect the entire communications system,
but it is in the channel where it can do the most
damage since this is where the signal is weakest.

RECEIVER

F After receiving the selected high-frequency modulated
signal, the receiver now will apply demodulation to
revert the signal to its original form.

DESTINATION

F The output of the receiver is fed into the circuit of the
desired destination.

Examples:

1. Picture tube of a television set
2. Speakers of a radio set
3. Computer
4. Telephone handset


BANDWIDTH

F The bandwidth of a signal refers to the width of the
band (or range) of frequencies occupied by a
particular signal.

F Bandwidth is very important in designing
communication systems since it dictates the type of
channel suitable for the transmission of a particular
signal.

F If the signal is composed of several sinusoidal signal
components, then

BW = highest frequency - lowest frequency

This equation is good for sinusoidal (sine or cosine)
waves only.

Example:

If the signal to be transmitted is composed of sine
waves ranging from 1,000 Hz to 5,000 Hz, then
the bandwidth is computed to be:

BW = 5,000 - 1,000 = 4,000 Hz


F However, most information or message signals are
complex nonsinusoidal aperiodic waveforms.

Example:

v(t)

t

F According to the studies of Jean Fourier, all
nonsinusoidal signals can be expressed in terms of its
constituent sine waves. In other words, all
nonsinusoidal signals actually consist of several sine
and/or cosine waves.

F These sinusoidal components comprise the frequency
spectrum of the signal.


F Some important points regarding the sinusoidal
components:

1. The frequency of each component is unique.

2. The number of frequency components is
infinite.

3. In theory, the bandwidth of a nonsinusoidal
signal is infinite.

4. As a general rule, the higher the frequency
of a component, the lower its amplitude.

5. The higher frequency components will have
very small amplitudes such that they may be
considered negligible.

6. Therefore, there will be a finite number of
significant components.

F The bandwidth of complex nonsinusoidal aperiodic
waveforms is just the difference between the lowest
frequency and the highest significant frequency.


F Case Study : The Human Voice

power

shows the sound power a
human vocal system can
produce at various
frequencies

freq
2000 4000 6000 8000 12000

This graph shows that the human voice is mainly
composed of analog periodic signals ranging from 0 Hz
to 12,000 Hz.

If a communications channel is to convey the entire
frequency range of human sounds, it must have a
minimum frequency near zero and a bandwidth of
more than 12,000 Hz.


F The Telephone System Bandwidth

Because of technology limitations and cost trade-offs
made during the design of the public telephone system,
this system can only handle a small part of the total
bandwidth of the human voice.

Telephone System Bandwidth = 300 Hz to 3,400 Hz

The 300 to 3,400 Hz range is sufficient to convey
messages to distant listeners. This range is the portion
of the voice bandwidth that can produce the greatest
power.


NOISE IN A COMMUNICATION SYSTEM

F Noise is any unwanted energy tending to interfere with
the signal to be transmitted.

Examples:

1. “Confetti” superimposed on the picture of a
television broadcast.
2. Hissing sound in a radio transmission.
3. A logic 0 becoming a logic 1 in computer
data transmission.

F Types of Noise:

1. External Noise. This is noise originating from
outside the communication system.

1.1. Atmospheric Noise. This type of noise is
mainly due to spurious radio waves that tend
to induce unwanted voltages in the antenna.
It is also known as static.

Example:
Lightning discharges during
thunderstorms.

Atmospheric noise is less disturbing for
transmissions using frequencies higher than
30 MHz.


1.2. Extraterrestrial Noise. This noise comes
from outer space.

Extraterrestrial Noise is divided into two
groups:

Solar Noise. Noise due to the intense
heat from the sun. This is most severe
during corona flares or sunspots.

Cosmic Noise or Blackbody Noise.
This is noise due to the distant stars.
What they lack in distance, they made
up for it in numbers.

Extraterrestrial noise is less noticeable at
frequencies below 20 MHz.

1.3. Man-Made Noise or Industrial Noise. This
noise is produced by man-made devices such
as automotive ignition, electrical motors,
fluorescent lights, and radiation from high-
voltage lines.


2. Internal Noise. This is noise originating from
within the communication system.

2.1. Thermal Agitation Noise or Johnson Noise
or White Noise. This noise is due to the
random and rapid movement of electrons in
any resistive component. Electrons “bump”
with each other.

2.2. Shot Noise. This noise is due to active
devices present in any communication
system.

It is caused by the random fluctuations in the
arrival of electrons or holes at the collector
of transistors.

When amplified, shot noise will sound like
lead shot falling over a metal surface.

2.3. Transit-time Noise. This noise is generated
in active devices. If the travel time of
electrons flowing from the emitter to the
collector becomes comparable to the period
of the signal, then some of these electrons
are diffused back to the collector.

This would cause the random
noise to be generated at the
input of the device.


2.4. Partition Noise. This noise is due to current
being divided between two or more paths.
The random variations in the division
process can cause fluctuations in current
thus generating noise.

2.5. Flicker Noise or Modulation Noise. This
noise is due to variations in current density
in semiconductors. This would cause
fluctuations in the conductivity of the device
which in turn would produce a varying
voltage drop when direct current flows.

Flicker noise is usually in the lower-
frequency range (a few KHz).

F Noise is fundamental. They are physically part of
nature and little can be done to totally eradicate them.
They can however, be minimized.

F In the study of noise, it is not important to know the
absolute value of noise. Even if the power of the noise
is very small, it may have a significant effect if the
power of the signal is also small.

F What is important is a comparison between noise and
the signal.


F The signal-to-noise ratio (SNR) or noise figure is the
ratio of signal power to noise power.

SNR = Ps / P n

Example:

Ps1 = 5 w Ps2 = 50,000 w

Pn1 = 50 mw Pn2 = 50 w

SNR1 = 5 / 50 x 10-3 SNR2 = 50,000 / 50
= 1,000 = 1,000

Both systems have the same performance.

F Ideally, SNR = ∞ (when Pn = 0). In practice, SNR
should be high as possible.

F An SNR ≥ 1,000 is acceptable.


F SNR can also be expressed in terms of voltage or
current.

Ps = V2s / Rs Pn = V2n / Rn

2
Vs
Ps R
SNR = = 2 s
Pn Vn
Rn

If Rs = Rn (which is true all the time), then:

antenna resistance

2
V 
SNR =  s 
 Vn 
 

For current:

2
I 
SNR =  s 
 In 
 


THE COMMUNICATIONS CHANNEL

F A communications channel is the physical or non-
physical connection between a transmitter and
receiver.

F A communications channel moves electromagnetic
energy between a source and one or more destination
points while retaining the information contained in the
energy when it leaves the source.

F Characteristics of an ideal channel:

1. It is a perfect vacuum. Therefore, there are
no physical objects that can reduce the level
of energy sent out by the transmitter. In
other words, there is no loss of signal
strength.

2. There are no errors.

3. Signals would travel at the speed of light
(300,000 km per second).

F The ideal channel does not exist.


F Types of Channels

1. Analog Channels. These channels can carry
analog or continuous signals. An analog signal
goes through all values within its range.

v v

t t

Examples: telephone system, commercial
radio system

2. Digital Channels. These channels can carry
digital or discrete signals. A digital signal can not
assume all of the possible values within its range.

v v

t t

Example: computer communications


COMMUNICATIONS CHANNEL CHARACTERISTICS

F Signal Attenuation

Attenuation is the fading of an electrical signal or
decrease in signal strength. This is primarily due to the
internal resistance of the channel.

F Electronic Noise

Electronic noise is any unwanted signal or voltage that
tends to interfere with the proper and easy reception
and reproduction of wanted signals. Noise can distort
signals beyond recognition.

F Channel Capacity

This refers to the quantity of information the channel
can convey over a given period.


ANALOG CHANNEL CAPACITY

F An aperiodic analog signal actually has several
periodic (sinusoidal) component signals called
frequency components. Each of these frequency
components has a different frequency and amplitude
or signal strength.

The frequency of a component is inversely
proportional to its signal strength. In other words, the
higher the frequency of a component, the lower is its
signal strength and vice-versa.

Some frequency components (particularly the ones
with very high frequency) have very small amplitudes
that they are already considered insignificant.

F The bandwidth of a signal is the difference between
the lowest and highest significant frequency of a single
analog signal.

F The bandwidth of a channel is the difference between
the lowest and highest frequency an analog channel
can convey to a distant receiver that the receiver can
understand.

F A broadband channel is a channel with a wide
bandwidth while a baseband channel is a channel with
a narrow bandwidth.

F THE CAPACITY OF AN ANALOG CHANNEL IS
ITS BANDWIDTH.

F Case Study : The Human Voice

power

shows the sound power a
human vocal system can
produce at various
frequencies

freq
2000 4000 6000 8000 12000

This graph shows that the human voice is mainly
composed of analog periodic signals ranging from 0 Hz
to 12,000 Hz.

If a communications channel is to convey the entire
frequency range of human sounds, it must have a
minimum frequency near zero and a bandwidth of
more than 12,000 Hz.


F The Telephone System Bandwidth

Because of technology limitations and cost trade-offs
made during the design of the public telephone system,
this system can only handle a small part of the total
bandwidth of the human voice.

Telephone System Bandwidth = 300 Hz to 3,400 Hz

The 300 to 3,400 Hz range is sufficient to convey
messages to distant listeners. This range is the portion
of the voice bandwidth that can produce the greatest
power.


DIGITAL CHANNEL CAPACITY

F In general, digital signals have two states (bits):

1. Logic 1 (mark) - 5 volts

2. Logic 0 (space) - 0 volt or -5 volts

F A communications channel that conveys a digital
signal has limitations that determine how often the
signal can change state over a given period.

F These limitations establish the maximum rate at which
data can flow through the channel.

F Channel Bit Rate

The capacity of a digital channel is the number of
digital values the channel can convey in one second.
It is usually measured in bits per second (bps).


F The bit period (or bit time) of a digital signal is the
length of 1 bit in seconds.

+v

1 0 1 1 0 0 1
t

-v

Bit Period

F The bit rate of a digital signal is the reciprocal of its bit
period (bit rate = 1 / bit period).

Example:

If the bit period of a digital signal is 0.208 ms,
then its bit rate is:

1 1
bit r ate = =
bit period 0.208 x 10- 3

bit rate = 4,800 bps


RELATIONSHIP BETWEEN BANDWIDTH AND DATA
RATE

F Digital signals consist of a large number of frequency
components. If digital signals are transmitted over a
channel with a limited bandwidth, only those
components that are within the bandwidth of the
transmission medium are received.

0 1 1 0 0 0 1 0
1

rms amplitude
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Time
1
1 Component

0
1

1
2 Components

0
1 2

1
4 Components

0
1 2 3 4

1
8 Components

0
1 2 3 4 5 6 7 8


F The faster the data rate of a digital signal, the higher
the bandwidth will be required since the frequency
components will be spaced farther apart.

F Therefore, a limited bandwidth will also limit the data
rate that can be used for transmission

F Nyquist derived a formula that determines the
maximum data rate of a transmission medium as a
function of its bandwidth:

2Blog (M )
C= 10
log 2
10

where C is the maximum data transfer rate of the
system in bits per second, B is the bandwidth of
the system in Hz, and M is the number of levels
per signalling element.


Example:

A digital signal that uses 2 levels per signalling
element is to be transmitted over a channel with a
bandwidth of 3000 Hz (similar to that of the
analog telephone system). What is the maximum
data rate that the system can have?

Solution:

B = 3,000 Hz

M = 2

2(3,000)log 2
C = 10
log 2
10

C = 6,000 bps

In practice, the data transfer rate will be less than
this because of other effects such as noise.


TRANSMISSION MEDIA

F Transmission channels can be classified as either
bounded or unbounded.

F In bounded channels, signals are confined to the
medium and do not leave it.

F In unbounded channels, the signals (electromagnetic
signals or radio waves) originated by the source travel
freely into the medium and spread throughout the
medium.

F Examples of bounded media:

1. Wire Pairs. This is the earliest and simplest type
of bounded media which provides a go and
return path for electrical signals.

Wire pairs have low attenuation of voice
frequencies due to the large size of the wire and
the large distance between the two wires when
mounted on the crossarm of a utility pole.

Example:

A 104 mil (0.104 inch) diameter open wire
line has a typical attenuation of 0.07 dB per
mile.


A decibel is simply a ratio of two powers.

Decibel = 10 log10 (P 2/P1)

where:
P2 = output power
P1 = input power

If a decibel value is positive, there is power gain
(amplification). If it is negative, there is power
loss (attenuation).

Example:

Attenuation = 0.07 dB per mile

-0.07 = 10 log10 (P 2/P1)
-0.007 = log10 (P 2/P1)
P2 / P 1 = 0.984
P2 = 0.984 P 1 (after 1 mile)

If the transmitted power (P1) is 1 W, then
the power at the receiving side (P2) will be
0.984 W.

The main problems associated with wire pairs are
interference from electromagnetic radiation and
crosstalk due to capacitive coupling.

Wire pairs can have a data rate not greater than
19.2 Kbps over a distance of about 50 m.

2. Twisted Pair Lines. This consists of two
insulated copper wires (typically 1 mm thick)
twisted together in a helical form so that each
wire faces the same amount of interference.

The twisting minimizes electromagnetic
interference to similar pairs close by and
therefore reduces noise. The more twists, the less
noise.

Twisted pair wires come in a wide range of
gauges.

Example:

A 19-gauge wire has a diameter of 0.03584
inch while a 26-gauge wire has a diameter of
0.01594 inch.

Most twisted pair wires consist of wire pairs
twisted together and made up into cables of 4 to
3,000 pairs.


The major problem of twisted-pair lines is that it
suffers from skin effect. As the frequency of the
signal being transmitted is increased, the signal
current tends to flow only on the outside portion
or surface of the wire.

This is the same as if the line resistance
has been increased at higher
frequencies causing such signals to be
attenuated.

Twisted pair lines can have bit rates in the order
of several Mbps over a distance of a few
kilometers.

There are two types of twisted pair wires:

1. Unshielded Twisted Pair (UTP)

There is no physical shielding, just an outer
jacket. Therefore, more twists are needed to
reduce noise.

This is the same type of cable used in
telephone lines.

It has a relatively small size thus making it
easy to install.

Category 3 UTP consist of two insulated
wires gently twisted together. Four such
pairs are typically grouped together in a
plastic sheath for protection and to keep the
eight wires together.

Starting at around 1988, the more advanced
Category 5 UTP were introduced. They are
similar to CAT 3 UTP, but with more twists
per centimeter and Teflon insulation, which
results in less crosstalk and a better quality
signal over longer distances, making them
more suitable for high-speed computer
communication.

2. Shielded Twisted Pair (STP)

This cable has an added shield of copper
braid around all the wire pairs. The entire
STP cable is also shielded (less noise but
more expensive than UTP).

STP has a large outside diameter which
makes it difficult to install.

STP can support faster data rates and longer
range than UTP.

This type of cable was introduced by IBM
for its token ring network.


3. Coaxial Cable. The ground and reference wires
take the form of a solid conductor running
concentrically (coaxially) inside a solid outer
circular conductor. The space between the two
conductors should ideally be filled with air, but in
practice it is normally filled with a dielectric
insulating material.

Braided Protective
Insulating outer plastic
Copper conductor
material covering
core

Due to its geometry, the center conductor is
effectively shielded from external interference
signals and also only minimal losses occur due to
electromagnetic radiation and the skin effect
(self-shielding).

Coax cables work well with frequencies from 100
KHz to 2 GHz (or even up to 10 GHz). Because
of the larger bandwidth, a faster data rate is
possible (up to 1 Gbps).


4. Fiber Optic Cables. These cables carry the
transmitted information in the form of a
fluctuating beam of light in a glass fiber.

Since it does not use electricity, there is no
electromagnetic radiation (good security). They
are essentially free from crosstalk and electrical
interference.

There is minimal attenuation since fiber optic
cables have low transmission losses which allows
a much greater separation between repeaters.

Light has a much higher frequency of operation
(800 THz). This higher bandwidth allows data
transmission rates of 20 Gbps and above and over
distances up to 30 Km.


Three (3) main components:

1. Transmission Medium. Ultra-thin fiber
of glass or fused silica.
2. Light Source. LED (Light Emitting
Diode) or laser diode which emit light
pulses when an electrical current is
applied to it
3. Detector. Photodiode which generates
an electrical pulse when light falls on it

Fiber cable types:

1. Multimode Fiber. This was designed
to trap light rays internally through light
refraction at different angles of
incidence. Multimode fiber uses LEDs.
2. Single Mode Fiber. This was designed
to be thin enough (one wavelength) to
avoid refraction (no bouncing) and thus
allowing a single light ray to pass.
Single mode fiber uses laser diode for
better focus resulting in higher
efficiency and longer reaches.

The main problems of fiber optics are its cost and
difficulty in installation.


F Examples of unbounded transmission:

1. High-Frequency Radio Transmission. Radio
transmission in the frequency band between 3
MHz and 30 MHz is called HF radio.

Electromagnetic Spectrum:

From To Name
3 KHz 30 KHz VLF
30 KHz 300 KHz LF
300 KHz 3 MHz MF
3 MHz 30 MHz HF
30 MHz 300 MHz VHF
300 MHz 3 GHz UHF
3 GHz 30 GHz SHF
30 GHz 300 GHz EHF


Propagation Paths of HF Radio Waves:

1. Ground Waves. The signal follows the
curvature of the earth’s surface (for
lower HF frequencies).

2. Sky Waves. The signal bounces back
and forth between the earth’s surface
and the various layers of the earth’s
ionosphere (for the higher HF
frequencies).

ionosphere
SKY
WAVE

GROUND
WAVE
surface of the earth


2. Microwave Radio Transmission. Microwave
refers to frequencies above the HF region.

Microwave signals follow line-of-sight (LOS)
propagation, and is therefore highly directional.
However, this limits the distance that can be
covered. To facilitate beyond-the-horizon
propagation, satellite or terrestrial repeaters are
used.


Due to a higher frequency of operation,
microwave systems carry large quantities of
information.

The required antenna is smaller due to shorter
wavelength (due to higher frequencies). Take
note that the size of the antenna required to
transmit a signal is proportional to the wavelength
(λ) of the signal.

λ = v/f

where: f = frequency of the signal

v = velocity of signal propagation,
usually near the speed of light
(3 x 108 m/s )

Example:

HF = 15 MHz

λ = 3 x 108 / 15 x 106 = 20 m

Microwave = 3 GHz

λ = 3 x 108 / 3 x 109 = 0.1 m


Problems with microwave systems:

1. Attenuated by solid objects (including earth)
and in addition, the higher frequencies are
attenuated by rain, snow and fog.

2. Reflected from flat conductive surfaces
(water, metal structures, etc.).

3. Diffracted (split) around solid objects.

4. Refracted (bent) by the atmosphere so that
the beam may travel beyond the line-of-sight
distance and be picked up by an antenna
that is not supposed to receive it.


INFORMATION THEORY

F Information Theory is a quantitative body of
knowledge that has been established about
information.

F Information is assigned a precise value if one is to deal
with it scientifically.

F The meaning of information is not important as
compared to the quantity of information.

F Information is a physical quantity such as mass.

Example:

1 kg. of gold has the same mass as 1 kg. of
garbage.

F Information theory is used to establish, precisely and
mathematically the rate of information issuing from
any source, the information capacity of the channel,
system or storage device, and the efficiency of codes.


F Information is defined as the choice of one message
out of set of finite messages.

meaning is immaterial

more choices means more information

when measuring information, it must be
taken into account that some choices
are more likely than others and
therefore contain less information

F The simplest possible choice is the one involving two
equally likely events.

In this case, it is convenient to use the information
content of this kind of choice as the basic unit of
information.

Thus the bit is defined as the quantity of information
required to permit the correct selection of one out of a
pair of equiprobable events.


Number of bits of information
which must be given to enable
the correct selection of one = log2 N
event from a set of N
equiprobable events

If the intelligence (or knowledge) to be
communicated can be represented in N
equally likely symbols, then the amount
of information required per symbol is
log2 N bits.

Examples:

1. If N = 16, then the number of bits required to
represent one of 16 possible choices or events is
log2 16 = 4 bits.

2. In ASCII, 7 bits are used which represent one
choice out of a total of 128 choices.

3. If the English alphabet is used (26 letters and 1
space character), then log2 27 = 4.76 bits are
required to represent one choice or one symbol.


F Not every symbol is equally likely to be used in a
given communication.

Example:

The letter E is more likely to occur than the letter
S.

F Any choice that has a high probability of occurring is
redundant and contains very little information.

Example:

The probability of the letter U following a letter Q
is almost 1. Therefore U is fully redundant in this
case and contains no information.

F However, redundancy is desirable in order to raise the
chances of receiving a good message when the
medium or channel is noisy.


Ii Communications Channel

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