Data Communication Principles

Data Communication Principles
Data Signals
Data Rate Limits
Performance
Digital to Digital Conversion
Digital to Analog Conversion
Transmission of Digital Data
Multiplexing

To be transmitted, data must be
transformed to electromagnetic signals.

ANALOG AND DIGITAL
Data can be analog or digital. The term analog data refers
to information that is continuous; digital data refers to
information that has discrete states. Analog data take on
continuous values. Digital data take on discrete values.

Analog and Digital Data
 Data can be analog or digital.
 Analog data are continuous and take
continuous values.
 Digital data have discrete states and take
discrete values.

Analog and Digital Signals
• Signals can be analog or digital.
• Analog signals can have an infinite number of
values in a range.
• Digital signals can have only a limited
number of values.

Figure Comparison of analog and digital signals

PERIODIC ANALOG SIGNALS
In data communications, we commonly use periodic
analog signals and nonperiodic digital signals.
Periodic analog signals can be classified as simple or
composite.
A simple periodic analog signal, a sine wave, cannot be
decomposed into simpler signals.
A composite periodic analog signal is composed of
multiple sine waves.

Figure Two signals with the same phase and frequency,
but different amplitudes

Frequency and period are the inverse of
each other.
Note

Figure Two signals with the same amplitude and phase,
but different frequencies

Table Units of period and frequency

The power we use at home has a frequency of 60 Hz. The period of this sine wave can be
determined as follows:
Example

The period of a signal is 100 ms. What is its frequency in kilohertz?
Example
Solution
First we change 100 ms to seconds, and then we calculate the frequency from the period
(1 Hz = 10−3 kHz).

Frequency
• Frequency is the rate of change with respect
to time.
• Change in a short span of time means high
frequency.
• Change over a long span of
time means low frequency.

If a signal does not change at all, its
frequency is zero.
If a signal changes instantaneously, its
frequency is infinite.
Note

Phase describes the position of the
waveform relative to time 0.
Note

Figure Three sine waves with the same amplitude and frequency,
but different phases

A sine wave is offset 1/6 cycle with respect to time 0. What is its phase in degrees and
radians?
Example
Solution
We know that 1 complete cycle is 360°. Therefore, 1/6 cycle is

Figure The time-domain and frequency-domain plots of a sine wave

A complete sine wave in the time domain
can be represented by one single spike in
the frequency domain.
Note

The frequency domain is more compact and useful when we are dealing with more
than one sine wave. For example, Figure 3.8 shows three sine waves, each with
different amplitude and frequency. All can be represented by three spikes in the
frequency domain.
Example

Figure The time domain and frequency domain of three sine waves

Signals and Communication
• A single-frequency sine wave is not
useful in data communications
• We need to send a composite signal, a
signal made of many simple sine
waves.
• According to Fourier analysis, any
composite signal is a combination of
simple sine waves with different
frequencies, amplitudes, and phases.

Bandwidth and Signal Frequency
• The bandwidth of a composite signal is
the difference between the highest and
the lowest frequencies contained in that
signal.

Figure The bandwidth of periodic and nonperiodic composite signals

If a periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500,
700, and 900 Hz, what is its bandwidth? Draw the spectrum, assuming all components
have a maximum amplitude of 10 V.
Solution
Let fh be the highest frequency, fl the lowest frequency, and B the bandwidth. Then
Example
The spectrum has only five spikes, at 100, 300, 500, 700, and 900 Hz (see Figure 3.13).

Figure The bandwidth for Example

A periodic signal has a bandwidth of 20 Hz. The highest frequency is 60 Hz. What is the
lowest frequency? Draw the spectrum if the signal contains all frequencies of the same
amplitude.
Solution
Let fh be the highest frequency, fl the lowest frequency, and B the bandwidth. Then
Example
The spectrum contains all integer frequencies. We show this by a series of spikes (see
Figure 3.14).

A nonperiodic composite signal has a bandwidth of 200 kHz, with a middle frequency of
140 kHz and peak amplitude of 20 V. The two extreme frequencies have an amplitude of
0. Draw the frequency domain of the signal.
Solution
The lowest frequency must be at 40 kHz and the highest at 240 kHz. Figure 3.15 shows
the frequency domain and the bandwidth.
Example

Fourier analysis is a tool that changes a
time domain signal to a frequency domain
signal and vice versa.
Note
Fourier Analysis

Time limited and Band limited Signals
• A time limited signal is a signal for which the
amplitude s(t) = 0 for t > T1 and t < T2
• A band limited signal is a signal for which the
amplitude S(f) = 0 for f > F1 and f < F2

DIGITAL SIGNALS
In addition to being represented by an analog signal, information can also be represented
by a digital signal. For example, a 1 can be encoded as a positive voltage and a 0 as zero
voltage. A digital signal can have more than two levels. In this case, we can send more
than 1 bit for each level.

Figure Two digital signals: one with two signal levels and the other
with four signal levels

A digital signal has eight levels. How many bits are needed per level? We calculate the
number of bits from the formula
Example
Each signal level is represented by 3 bits.

A digital signal has nine levels. How many bits are needed per level? We calculate the
number of bits by using the formula. Each signal level is represented by 3.17 bits.
However, this answer is not realistic. The number of bits sent per level needs to be an
integer as well as a power of 2. For this example, 4 bits can represent one level.
Example

Assume we need to download text documents at the rate of 100 pages per sec. What is
the required bit rate of the channel?
Solution
A page is an average of 24 lines with 80 characters in each line. If we assume that one
character requires 8 bits (ascii), the bit rate is
Example

Figure The time and frequency domains of periodic and nonperiodic
digital signals

A digital signal is a composite analog signal
with an infinite bandwidth.
Note

Figure Baseband transmission using a dedicated medium

DATA RATE LIMITS
A very important consideration in data communications is how fast we can send data, in
bits per second, over a channel. Data rate depends on three factors:
1. The bandwidth available
2. The level of the signals we use
3. The quality of the channel (the level of noise)

Capacity of a System
• The bit rate of a system increases with an increase
in the number of signal levels we use to denote a
symbol.
• A symbol can consist of a single bit or “n” bits.
• The number of signal levels = 2n.
• As the number of levels goes up, the spacing
between level decreases -> increasing the
probability of an error occurring in the presence
of transmission impairments.

Nyquist Theorem
• Nyquist gives the upper bound for the bit rate of a
transmission system by calculating the bit rate
directly from the number of bits in a symbol (or
signal levels) and the bandwidth of the system
(assuming 2 symbols/per cycle).
• Nyquist theorem states that for a noiseless
channel:
C = 2 B log22n
C= capacity in bps
B = bandwidth in Hz

Consider a noiseless channel with a bandwidth of 3000 Hz transmitting a signal with two
signal levels. Calculate maximum bit rate.
Example

Consider the same noiseless channel transmitting a signal with four signal levels (for each
level, we send 2 bits). Calculate the maximum bit rate.
Example

We need to send 265 kbps over a noiseless channel with a bandwidth of 20 kHz. How
many signal levels do we need?
Example

Shannon’s Theorem
• Shannon’s theorem gives the capacity of a
system in the presence of noise.
C = B log2(1 + SNR)

Consider an extremely noisy channel in which the value of the signal-to-noise ratio is
almost zero. In other words, the noise is so strong that the signal is faint. For this channel
calculate the capacity C.
Example
This means that the capacity of this channel is zero regardless of the bandwidth. In other
words, we cannot receive any data through this channel.

A telephone line normally has a bandwidth of 3000. The signal-to-noise ratio is usually
3162. For this channel calculate the capacity.
Example

The signal-to-noise ratio is often given in decibels. Assume that SNRdB = 36 and the
channel bandwidth is 2 MHz. Calculate channel capacity.
Example

We have a channel with a 1-MHz bandwidth. The SNR for this channel is 63. What are the
appropriate bit rate and signal level?
Example

The Shannon formula gives us 6 Mbps, the upper limit. For better performance we
choose something lower, 4 Mbps, for example. Then we use the Nyquist formula to find
the number of signal levels.
Example (continued)

The Shannon capacity gives us the upper
limit; the Nyquist formula tells us how many
signal levels we need.
Note

PERFORMANCE
One important issue in networking is the performance of the network—how good is it?. In
this section, we introduce terms that we need for future chapters.

In networking, we use the term bandwidth
in two contexts.
 The first, bandwidth in hertz, refers to the range of frequencies in a
composite signal or the range of frequencies that a channel can pass.
 The second, bandwidth in bits per second, refers to the speed of bit
transmission in a channel or link. Often referred to as Capacity.
Note

A network with bandwidth of 10 Mbps can pass only an average of 12,000 frames per
minute with each frame carrying an average of 10,000 bits. What is the throughput of this
network?
Example
The throughput is almost one-fifth of the bandwidth in this case.

Propagation & Transmission delay
• Propagation speed - speed at which a bit
travels though the medium from source to
destination.
• Transmission speed - the speed at which all
the bits in a message arrive at the
destination. (difference in arrival time of
first and last bit)

Propagation and Transmission Delay
• Propagation Delay = Distance/Propagation speed
• Transmission Delay = Message size/bandwidth bps
• Latency = Propagation delay + Transmission delay +
Queueing time + Processing time

What is the propagation time if the distance between the two points is 12,000 km?
Assume the propagation speed to be 2.4 × 10^8 m/s in cable.
Example

What are the propagation time and the transmission time for a 2.5-kbyte message (an e-
mail) if the bandwidth of the network is 1 Gbps? Assume that the distance between the
sender and the receiver is 12,000 km and that light travels at 2.4 × 108 m/s.
Example

Note that in this case, because the message is short and the bandwidth is high, the
dominant factor is the propagation time, not the transmission time. The transmission
time can be ignored.
Example (continued)

What are the propagation time and the transmission time for a 5-Mbyte message (an
image) if the bandwidth of the network is 1 Mbps? Assume that the distance between the
sender and the receiver is 12,000 km and that light travels at 2.4 × 108 m/s.
Example

Note that in this case, because the message is very long and the bandwidth is not very
high, the dominant factor is the transmission time, not the propagation time. The
propagation time can be ignored.
Example (continued)

Figure Concept of bandwidth-delay product

The bandwidth-delay product defines the
number of bits that can fill the link.
Note

DIGITAL-TO-DIGITAL CONVERSION
In this section, we see how we can represent digital
data by using digital signals. The conversion involves
three techniques: line coding, block coding, and
scrambling. Line coding is always needed; block
coding and scrambling may or may not be needed.

Line Coding
• Converting a string of 1’s and 0’s (digital
data) into a sequence of signals that denote
the 1’s and 0’s.
• For example a high voltage level (+V) could
represent a “1” and a low voltage level (0 or
-V) could represent a “0”.

Figure Line coding and decoding

Mapping Data symbols onto
Signal levels
• A data symbol (or element) can consist of a
number of data bits:
– 1 , 0 or
– 11, 10, 01, ……
• A data symbol can be coded into a single signal
element or multiple signal elements
– 1 -> +V, 0 -> -V
– 1 -> +V and -V, 0 -> -V and +V
• The ratio ‘r’ is the number of data elements
carried by a signal element.

Relationship between data rate and
signal rate
• The data rate defines the number of bits sent per
sec - bps. It is often referred to the bit rate.
• The signal rate is the number of signal elements
sent in a second and is measured in bauds. It is
also referred to as the modulation rate.
• Goal is to increase the data rate while reducing
the baud rate.

Figure Signal element versus data element

Considerations for choosing a good line
encoding
• Baseline wandering - a receiver will evaluate the
average power of the received signal (called the
baseline) and use that to determine the value of
the incoming data elements. If the incoming signal
does not vary over a long period of time, the
baseline will drift and thus cause errors in
detection of incoming data elements.
• A good line encoding scheme will prevent long
runs of fixed amplitude.

Line encoding C/Cs
• DC components - when the voltage level
remains constant for long periods of time,
there is an increase in the low frequencies
of the signal. Most channels are bandpass
and may not support the low frequencies.
• This will require the removal of the dc
component of a transmitted signal.

Line encoding C/Cs
• Self synchronization - the clocks at the
sender and the receiver must have the
same bit interval.
• If the receiver clock is faster or slower it will
misinterpret the incoming bit stream.

Figure Effect of lack of synchronization

Line encoding C/Cs
• Error detection - errors occur during
transmission due to line impairments.
• Some codes are constructed such that
when an error occurs it can be detected.
For example: a particular signal transition is
not part of the code. When it occurs, the
receiver will know that a symbol error has
occurred.

Line encoding C/Cs
• Noise and interference - there are line
encoding techniques that make the
transmitted signal “immune” to noise and
interference.
• This means that the signal cannot be
corrupted, it is stronger than error
detection.

Line encoding C/Cs
• Complexity - the more robust and resilient
the code, the more complex it is to
implement and the price is often paid in
baud rate or required bandwidth.

Unipolar
• All signal levels are on one side of the time axis -
either above or below
• NRZ - Non Return to Zero scheme is an example of
this code. The signal level does not return to zero
during a symbol transmission.
• Scheme is prone to baseline wandering and DC
components. It has no synchronization or any
error detection. It is simple but costly in power
consumption.

Polar - NRZ
• The voltages are on both sides of the time axis.
• Polar NRZ scheme can be implemented with two
voltages. E.g. +V for 1 and -V for 0.
• There are two versions:
– NRZ - Level (NRZ-L) - positive voltage for one symbol
and negative for the other
– NRZ - Inversion (NRZ-I) - the change or lack of change in
polarity determines the value of a symbol. E.g. a “1”
symbol inverts the polarity a “0” does not.

Figure Polar NRZ-L and NRZ-I schemes

In NRZ-L the level of the voltage
determines the value of the bit.
In NRZ-I the inversion
or the lack of inversion
determines the value of the bit.
Note

NRZ-L and NRZ-I both have a DC
component problem and baseline
wandering, it is worse for NRZ-L. Both
have no self synchronization &no error
detection. Both are relatively simple to
implement.
Note

Polar - RZ
• The Return to Zero (RZ) scheme uses three
voltage values. +, 0, -.
• Each symbol has a transition in the middle. Either
from high to zero or from low to zero.
• This scheme has more signal transitions (two per
symbol) and therefore requires a wider
bandwidth.
• No DC components or baseline wandering.
• Self synchronization - transition indicates symbol
value.
• More complex as it uses three voltage level. It has
no error detection capability.

Polar - Biphase: Manchester and
Differential Manchester
• Manchester coding consists of combining the
NRZ-L and RZ schemes.
– Every symbol has a level transition in the middle: from
high to low or low to high. Uses only two voltage levels.
• Differential Manchester coding consists of
combining the NRZ-I and RZ schemes.
– Every symbol has a level transition in the middle. But
the level at the beginning of the symbol is determined
by the symbol value. One symbol causes a level change
the other does not.

Figure Polar biphase: Manchester and differential Manchester schemes

In Manchester and differential
Manchester encoding, the transition
at the middle of the bit is used for
synchronization.
Note

The minimum bandwidth of Manchester
and differential Manchester is 2 times
that of NRZ. The is no DC component
and no baseline wandering. None of
these codes has error detection.
Note

Bipolar - AMI and Pseudoternary
• Code uses 3 voltage levels: - +, 0, -, to represent
the symbols (note not transitions to zero as in RZ).
• Voltage level for one symbol is at “0” and the
other alternates between + & -.
• Bipolar Alternate Mark Inversion (AMI) - the “0”
symbol is represented by zero voltage and the “1”
symbol alternates between +V and -V.
• Pseudoternary is the reverse of AMI.

Figure Bipolar schemes: AMI and pseudoternary

Block Coding
• For a code to be capable of error detection, we need to
add redundancy, i.e., extra bits to the data bits.
• Synchronization also requires redundancy - transitions are
important in the signal flow and must occur frequently.
• Block coding is done in three steps: division, substitution
and combination.

Block coding is normally referred to as
mB/nB coding;
it replaces each m-bit group with an
n-bit group.
Note

Scrambling
• The best code is one that does not increase the
bandwidth for synchronization and has no DC
components.
• Scrambling is a technique used to create a
sequence of bits that has the required features for
transmission - self clocking, no low frequencies, no
wide bandwidth.
• It is implemented at the same time as encoding,
the bit stream is created on the fly.
• It replaces ‘unfriendly’ runs of bits with a violation
code that is easy to recognize.

Figure AMI used with scrambling

For example: B8ZS substitutes eight
consecutive zeros with 000VB0VB.
The V stands for violation, it violates the
line encoding rule
B stands for bipolar, it implements the
bipolar line encoding rule

Figure Two cases of B8ZS scrambling technique

HDB3 substitutes four consecutive
zeros with 000V or B00V depending
on the number of nonzero pulses after
the last substitution.
If # of non zero pulses is even the
substitution is B00V to make total # of
non zero pulse even.
If # of non zero pulses is odd the
substitution is 000V to make total # of
non zero pulses even.

Figure Different situations in HDB3 scrambling technique

DIGITAL-TO-ANALOG CONVERSION
Digital-to-analog conversion is the process of changing
one of the characteristics of an analog signal based on
the information in digital data.

Digital to Analog Conversion
• Digital data needs to be carried on an
analog signal.
• A carrier signal (frequency fc) performs the
function of transporting the digital data in
an analog waveform.
• The analog carrier signal is manipulated to
uniquely identify the digital data being
carried.

Figure Digital-to-analog conversion

Figure Types of digital-to-analog conversion

Bit rate, N, is the number of bits per second (bps). Baud rate is the number of signal
elements per second (bauds).
In the analog transmission of digital data, the signal or baud rate is less than
or equal to the bit rate.
S=Nx1/r bauds
Where r is the number of data bits per signal element.
Note

An analog signal carries 4 bits per signal element. If
1000 signal elements are sent per second, find the bit
rate.
Solution
In this case, r = 4, S = 1000, and N is unknown. We can
find the value of N from
Example

Amplitude Shift Keying (ASK)
• ASK is implemented by changing the amplitude of
a carrier signal to reflect amplitude levels in the
digital signal.
• For example: a digital “1” could not affect the
signal, whereas a digital “0” would, by making it
zero.

Figure Binary amplitude shift keying

Figure Implementation of binary ASK

Frequency Shift Keying
• The digital data stream changes the
frequency of the carrier signal, fc.
• For example, a “1” could be represented by
f1=fc +f, and a “0” could be represented by
f2=fc-f.

Figure Binary frequency shift keying

Phase Shift Keyeing
• We vary the phase shift of the carrier signal
to represent digital data.
• PSK is much more robust than ASK as it is
not that vulnerable to noise, which changes
amplitude of the signal.

Figure Binary phase shift keying

Quadrature PSK
• To increase the bit rate, we can code 2 or more
bits onto one signal element.
• In QPSK, we parallelize the bit stream so that
every two incoming bits are split up and PSK a
carrier frequency. One carrier frequency is phase
shifted 90o from the other - in quadrature.
• The two PSKed signals are then added to produce
one of 4 signal elements. L = 4 here.

Figure QPSK and its implementation

Bandwidth utilization is the wise use of
available bandwidth to achieve
specific goals.
Efficiency can be achieved by multiplexing; i.e., sharing of the bandwidth between
multiple users.
Note

MULTIPLEXING
Whenever the bandwidth of a medium linking two
devices is greater than the bandwidth needs of the
devices, the link can be shared. Multiplexing is the set of
techniques that allows the (simultaneous) transmission
of multiple signals across a single data link. As data and
telecommunications use increases, so does traffic.

Figure Dividing a link into channels

Figure Categories of multiplexing

Figure Frequency-division multiplexing (FDM)

FDM is an analog multiplexing technique that combines analog signals.
It uses the concept of modulation.
Note

Figure FDM demultiplexing example

Figure Wavelength-division multiplexing (WDM)

WDM is an analog multiplexing technique to combine optical signals.
Note

Figuree Prisms in wavelength-division multiplexing and demultiplexing

Figure Time Division Multiplexing (TDM)

TDM is a digital multiplexing technique for combining several low-rate digital
channels into one high-rate one.
Note

Data Rate Management
• Not all input links maybe have the same
data rate.
• Some links maybe slower. There maybe
several different input link speeds
• There are three strategies that can be used
to overcome the data rate mismatch:
multilevel, multislot and pulse stuffing

Data rate matching
• Multilevel: used when the data rate of the input
links are multiples of each other.
• Multislot: used when there is a GCD between the
data rates. The higher bit rate channels are
allocated more slots per frame, and the output
frame rate is a multiple of each input link.
• Pulse Stuffing: used when there is no GCD
between the links. The slowest speed link will be
brought up to the speed of the other links by bit
insertion, this is called pulse stuffing.

Figure Multilevel multiplexing

Figure Multiple-slot multiplexing

Data Communication Principles

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