IT 318 – Supplementary Material Chapter 6
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IT 318 – SUPPLEMENTARY MATERIAL CHAPTER 6
Digital Communications
V. 2016
BARRY M. LUNT
Brigham Young University
IT 318 – Supplementary Material Chapter 6
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Table of Contents
Chapter 6: Digital Communications ............................................................................................................ 3
6.1 Overview: A Modern Miracle ........................................................................................................... 3
6.2 EM Spectrum and Bandwidth: Where and How Much? ................................................................... 3
6.3 Modulation: Putting Information on a Carrier ................................................................................... 4
6.4 Shannon’s Law: The Ultimate Speed Limit ...................................................................................... 5
6.5 Media: Our Three Options ................................................................................................................. 6
6.6 Analog to Digital Conversion: Entering a New Domain ................................................................... 7
6.7 Digital Tricks: The Wonders Digital Can Do for Us ......................................................................... 8
6.8 Networking: The Backbone of Computer Communication ............................................................. 12
6.9 The Internet: History of a Modern Marvel ...................................................................................... 14
6.10 Wireless: The Ultimate in Connectivity Convenience .................................................................. 16
6.11 Automation Standards: Performance and Convenience ................................................................ 16
Summary ................................................................................................................................................ 17
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Chapter 6: Digital Communications
6.1 Overview: A Modern Miracle Modern digital communications are truly ubiquitous; there is hardly any segment of our lives that is
untouched by them, in major ways. We have grown accustomed to instantly knowing what is taking place in any
corner of the world; to having cell-phone and internet service nearly everywhere we are; to being able to connect
with nearly anyone, any time. But prior to 1830, none of these technologies even existed; for thousands of years,
the fastest means of communication was a messenger on a horse. To say that has changed dramatically is the
understatement of the century.
This chapter is a very high-level overview of some of the fundamental technologies that underlie all of
this modern miracle. As desirable as it would be to dig into the many topics of this chapter in greater depth, we
will have to content ourselves with a basic overview, and acknowledge the presence of a great deal of further
information, readily available to the interested reader.
This author’s favorite example of our ability to communicate digitally is epitomized by the Voyager 1 and
2 deep space probes, launched by the USA in 1977. These probes successfully flew by Jupiter and Saturn, sending
back incredible pictures and discovering many new moons. Then the mission of Voyager 2 was extended, and it
visited the outer planets of Uranus and Neptune, over 2 billion miles distant from Earth. This was clear back in
about 1990. Today both probes are still transmitting and receiving data, though this data must travel more than 30
hours at the speed of light to reach Earth. The received signal strength is a vanishingly small 0.1 aW, or 1.0 x 10-19
W. Every trick in our digital communications book has been used to make this possible, and many of these tricks
will be overviewed in this chapter.
6.2 EM Spectrum and Bandwidth: Where and How Much? All electronic communication takes place by sending a changing voltage over a carrier – the changing
voltage is the information, while the carrier is the signal which, as implied by the term, carries the information
from A (the source) to B (the destination). What is the nature of the carrier? It is an electromagnetic (EM) wave,
of which
light is the
most familiar
example.
Figure 6.1 is
a reminder of
the many
known
components
of the EM
spectrum; it
represents all
there is
available to
us to send
EM signals.
Note
that the
frequency of an EM signal is the single identifying characteristic of an EM signal which places it on this
Figure 6.1: The electromagnetic (EM) spectrum represents the “space” available to us to send EM
signals.
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spectrum. It is also important to remember that the energy of a photon (a carrier of EM energy) is directly
proportional to its frequency: a photon at 1 THz possesses 1,000 times more energy than a photon at 1 GHz.
Because the EM spectrum covers more than 24 orders of magnitude, that also means that Gamma ray photons can
carry 1024 times more energy than a photon down in the VLF (Very Low Frequency) range – a phenomenal
amount!
Figure 6.1 can give us the impression that there is more than enough spectrum to send all our EM signals.
This would be true, if we had the ability to use all of it. To transmit data on EM waves (or are they particles?)
requires that we have some device which can produce these waves, another device which can put the data on these
waves (these are part of the transmitter, or A), and another device (part of B) which can detect these waves and
the data they carry. Today this is done with electronic transistors and diodes, along with other associated
electronic parts such as resistors, capacitors, and inductors, in what designers refer to as electronic circuits. So, we
presently are limited to those portions of the EM spectrum where we have been able to produce such circuits. This
includes the frequencies up to about 100 GHz, then those whose wavelength is from about 400-2000 nm, which
includes infrared and visible light. Much work is being done today on creating devices capable of working in the
“TeraHertz Gap”, generally defined as those frequencies between 200 GHz and 100 THz (about 2000 nm), but
this work is progressing only slowly. No significant work is being done on producing devices which can operate
in the ultraviolet, x-ray, or gamma-ray regions, for reasons that will not be discussed in this chapter.
The take-away of the preceding chapter is that despite the availability of a virtually unlimited amount of
spectrum, that portion of the EM spectrum which can be practically put to use today is somewhat limited, and
spectrum crowding is a serious issue today, one which is receiving much attention – and great progress is being
made.
Bandwidth is a term heavily used today, and which has a very specific meaning in digital
communications. Basically, it means the amount of EM spectrum which a given signal occupies. Using a traffic
analogy, let’s imagine a highway without marked lanes, in which each
item traveling on the highway uses only the width of the highway
necessary. Pedestrians and bicyclists would occupy much less width than
cars, and trucks and wide loads would occupy much more. In this traffic
analogy, the width of the road occupied by the bicycle, car, truck, or wide
load would be its bandwidth, and the highway would be the usable part of
the EM spectrum. Table 6.1 gives the required native bandwidth of
several common communication signals today.
6.3 Modulation: Putting Information on a Carrier Let’s start this section with an analogy to sending information
over a rope. A and B wish to communicate with each other, using nothing but a rope between them. First, they
must establish a connection – both A and B must be holding the rope, or at least looking at it, and the rope must
be free to move. The next thing A and B would have to do is to establish some kind of agreement as to the
meaning of the movements of the rope – what we know as a protocol. The point is this: if A and B are both
holding the rope, but the rope is not moving, the only thing B is getting from A is the carrier – the simple
information that A is ready to send something to B. The only way A can send information is if A moves the rope
in some fashion, and B knows what those movements mean.
Table 6.1: Some common EM
signals and their required native
bandwidth.
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In electronic communication, the carrier is an EM sine wave, of a specific nominal frequency. In order for
this carrier to send information, it must be modulated in some fashion, just as the rope in the previous paragraph
must be moved. Modulation is the act of
changing some feature of the EM sine wave. A
sine wave is characterized in only 3 ways: its
amplitude, its frequency, and its phase. These
are shown in Figure 6.2. Using the black sine
wave as our reference, we can see that the red
sine wave differs only in its amplitude; the
light blue sine wave differs only in its
frequency, and the green sine wave differs
only in its phase.
Thus, for EM signals, the only types
of modulation available to us are
amplitude modulation (AM), frequency
modulation (FM), and phase modulation
(PM or sometimes ϕM). Each of these
three types of modulation has its
respective characteristics, some of them
advantages and others disadvantages.
These characteristics are summarized in
Table 6.2. All 3 types of modulation are
widely used in modern digital
communication.
There is another entry in Table 6.2 that requires additional explanation: Digital M(odulation). In the
digital domain, we are still restricted to the 3 basic types of modulation, but because the carrier is modulated to
discrete values (this is what digital means, when it comes to modulation) of amplitude, frequency or phase, we
gain many advantages not available with only analog modulation; more on this later.
6.4 Shannon’s Law: The Ultimate Speed Limit
Shannon’s Law (named after Claude Shannon, who first wrote about it in his paper,
“Communication in the presence of noise”, published in 1949), is referred to here as an ultimate speed
limit. This is because it defines the absolute maximum error-free data rate that can be achieved in a
given channel, with a given signal-to-noise ratio. Unlike a traffic speed limit, in which we simply risk
being fined if we exceed that limit, the limit expressed by Shannon’s Law is a physical limit – we are
never able to exceed it. And in fact, we are never actually able to reach it, though recent advances have
come incredibly close to that limit.
There are three variables in Shannon’s Law: bandwidth, signal amplitude, and noise amplitude.
The equation that relates these variables to the maximum error-free capacity of the channel is given in
Equation 6.1, Shannon’s Law: 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 = 𝐵𝑊 ∗ 𝑙𝑜𝑔2(1 +𝑆
𝑁) (Eqn 6.1)
In Equation 6.1, the capacity is given in bits-per-second (also known bps, or b/s); the BW is
given in Hertz, and the Signal and Noise are always in the same units as each other: either Voltage or
Watts. As for finding the log2, since most calculators don’t have that function built in, recall that:
Figure 6.2: The three properties of a sine wave.
Table 6.2: The types of modulation and their respective characteristics.
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𝑙𝑜𝑔𝑛 𝑥 =𝑙𝑜𝑔10𝑥
𝑙𝑜𝑔10𝑛 (Eqn 6.2)
So, for log2, this means the log2 of 64 would be:
𝑙𝑜𝑔264 =𝑙𝑜𝑔1064
𝑙𝑜𝑔102=
1.8062
0.3010= 6.0 (Eqn 6.3)
Log2(64) is just a mathematical way of saying, “What power of 2 equals 64?”, so the answer of 6 seems
rather obvious, since we know that 26 = 64. Extending our understanding of Equation 6.1, let’s find the
capacity of a typical phone line, where the BW = 3kHz, the signal = 10W, and the noise = 5 mW:
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 = 3 𝑘𝐻𝑧 ∗ 𝑙𝑜𝑔2 (1 +10𝑊
5𝑚𝑊) = 3𝑘𝐻𝑧 ∗ 10.9665 = 𝟑𝟐. 𝟖𝟗𝟗𝒌𝒃/𝒔 (Eqn 6.4)
Increasing the bandwidth increases the capacity by the exact same proportion. Increasing the signal or
decreasing the noise also increases our capacity, but not at the same rate as increasing our bandwidth
since they are within the log2 part of the equation.
Another very important takeaway from Shannon’s Law is that if we want to increase the capacity
of a channel, we have only three options: increase our bandwidth, or increase our signal, or decrease the
noise in the channel.
A final look at Shannon’s Law is in Table 6.3. In
this table, the first row gives a capacity of 485.1 kb/s for the
given bandwidth, signal power, and noise power. The
second through fourth rows show the (log2) effect of an
increase in the noise power; each row has a 10x increase in
noise power, compared to the previous row. This results in a
13.7%, 15.8%, and 18.7% decrease in capacity, compared to
each previous row. Increasing bandwidth, however, has a
direct effect on the capacity, as shown in the last three rows.
Each of these rows has a 10x increase in the bandwidth, first
compared to the top row, then to the row immediately above it. The capacity increases by 10x each time,
showing this direct relationship.
6.5 Media: Our Three Options
In sending data from A to B, there are only three options for media: wired, wireless, or optical
fiber. Each medium has
its own characteristics,
including advantages and
disadvantages.
Additionally, there are
two main types of wired
media, and three main
ranges of wireless
frequencies. All of these
media are summarized in
Table 6.4.
Table 6.3: Several solutions of Shannon’s
Law equation, showing the effects of varying
signal strength and bandwidth.
Table 6.4: Media Characteristics
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As is nearly always the case, there is no best solution, and the media choice for a given situation
will depend on many factors, involving tradeoffs in most categories. This is why we have
communication systems using all of these media.
A few terms in Table 6.4 deserve clarification. RF stands for Radio Frequencies, a term coined
many decades ago to apply to the frequencies from about 500 kHz to about 1 GHz. Reach means the
distance between A and B, with no repeaters or amplifiers in between. EMI stands for ElectroMagnetic
Interference, and refers to the fact that electromagnetic (EM) waves are all around us today; the presence
of these EM waves pose an interference problem to media which are susceptible to this.
6.6 Analog to Digital Conversion: Entering a New Domain The real world we live in is dominated by analog things. Analog, in this case, simply means that
it varies continuously. Some examples include the height and weight of humans; the size of a tree or a
leaf on a tree; the temperature; the amount of sunlight; the velocity of the wind; music; vision.
Computers live in a digital world, dominated by 1s and 0s. Digital, in this case, simply means
that it varies in discrete increments. Some examples include the number of coins a person has; the
amount of money in your account; the number of people in a room; the number of cars on the highway;
the number of paper clips in a box. These things cannot vary continuously.
Any time we want to take something inherently analog and represent it or store it in a digital
world, it must first be converted from analog to digital. An example of an analog wave (in red), along
with a crude digital version of it (in blue) is
shown in Figure 6.3. There are two factors that
determine how faithfully the digital waveform
represents the original analog waveform: 1) how
frequently the waveform is sampled, and 2) how
small the step size needs to be. In the analog
world, the signal is continuous – not sampled.
Also, it can change continuously – not in discrete
increments (steps). For the digital world to fully
represent the analog world, we would have to
sample at nearly an infinite rate, and the step size
would have to be as small as a quantum energy packet, or about 6.626 x 10-34 J∙s, which is impossibly
small. And by the way, step size is also referred to as quantization error.
As in most engineering and technology decisions, the question we must answer is not what does
it take to do it perfectly, but what does it take to do it well enough? As for the first factor in analog to
digital conversion (the sampling rate), Harry Nyquist (1889-1976) gave us the answer that has since
been known as the Nyquist criterion: the signal must be sampled ≥2x the bandwidth of the signal, or
sometimes also stated as ≥2x the highest frequency. So if we consider music (see Table 6.1), in which
the bandwidth is 20 kHz, the Nyquist criterion states that we must sample music ≥40,000 times/sec in
order to adequately reproduce it. And by the way, in converting music to digital, the decision was made
to sample it at a rate of 44.1 ks/s (samples/second), which does meet this criterion.
The other factor (how small the step size needs to be) has been answered experimentally in most
applications. This means that a digital signal with a given step size is tested and compared to the original
Figure 6.3: An example of an analog waveform (in blue),
along with a rather crude digital version of the same
waveform (in red).
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analog signal; when the difference between the two signals becomes insignificant, the step size has been
determined. The equation for step size is given by equation 6.5:
𝑆𝑡𝑒𝑝 𝑆𝑖𝑧𝑒 =𝑉𝑚𝑎𝑥−𝑉𝑚𝑖𝑛
2𝑛 (Eqn 6.5)
where n = the number of bits, and (Vmax – Vmin) = the range of the signal being converted. Again using
the example of music, the number of bits adequate for high-quality storage and reproduction has been
determined to be 16 bits. Thus, the step size for a 20 Volt range is:
𝑆𝑡𝑒𝑝 𝑆𝑖𝑧𝑒 =20 𝑉
216 =20 𝑉
65536= 305.18 µ𝑉 (Eqn 6.6)
Table 6.5 gives the sampling rates and
resolution (number of bits, and percentage or ppm)
that have been deemed adequate for converting
several common analog signals into digital.
To transmit a signal which has been
converted from analog to digital, we must send each
sample, (each sample being of the designated
number of bits), and send them as fast as they are
being generated. For voice, this means our data
stream is: 8 ksamples/s * 8 bits/sample; when multiplied, the samples cancel out and we are left with 64
kbits/s – the standard data rate for transmitting voice. Note that a much higher data rate is necessary for
video: NTSC requires 5.5 Msamples/s * 24 bits/sample (since there are 3 colors), giving 132 Mbits/s;
HDTV requires even more at: 24 Msamples/sm * 24 bits/sample, giving 576 Mbits/s. This is the native
bandwidth requirements of these signals; compression has worked wonders on these very high data rate
requirements, but more on that in the next section.
6.7 Digital Tricks: The Wonders Digital Can Do for Us
There are several amazing things that we can do with digital signals, which we cannot do with
analog signals. These include compression, error detection and correction, and encryption, all of which
are used extensively in digital communication today.
6.7.1: Compression
There are two main categories of compression: lossless and lossy. Each has its respective
advantages and disadvantages.
Lossless compression is accomplished by finding repeating patterns in the data and replacing
these patterns with a simple code for each. On the other end of the transmission (the receiver end), the
data can then be restored to its original bits, using the table of special codes for patterns. Thus, no data is
lost. This is essential for transmitting financial data, spreadsheets, text files, and any data where lost bits
can be problematic. The disadvantage of lossless compression is that the maximum compression is only
about 2:1, which helps, but not enough in most cases. Examples of files extensions that been compressed
using lossless compression include .zip, .png, .gif., .wav, and JPEG 2000. Another fact regarding
lossless compression is that if one compresses a file a second time, no additional file size reduction is
accomplished.
Table 6.5: Sampling rates and resolution for converting
some common analog signals to digital.
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Lossy compression is accomplished in three main ways: spatial, temporal, and mathematical.
Additionally, there are lossy compression efforts that combine two or all three of these ways. The big
advantage of lossy compression is that huge compression ratios are possible: up to and even greater than
1000:1. The big disadvantage is that at the receiver end of the transmission, the file cannot be restored to
its original bits – some quality is lost. While this doesn’t sound useful, it has turned out to be highly
useful for signals such as video and music, which have very high native data rates. We have learned to
tolerate some reduction in the quality of these signals, in return for the greatly reduced data rates made
possible by lossy compression. It should also be mentioned that compression also reduces the amount of
storage needed to store the files.
Spatial lossy compression takes advantage of the fact that video signals are made up of scan lines
on the screen, and that some portions of the image are very similar. Particularly, the second scan line of
an image is not a great deal different from the first scan line; by taking advantage of this fact, we can
reduce the second scan line to a repeat of the first, with all necessary differences. The same is true for
subsequent scan lines – sending only the differences from the previous scan line saves a lot of bits.
Temporal lossy compression takes advantage of the fact that each frame of a video signal is not a
great deal different from the previous frame, received 1/30th or 1/60th of a second earlier. By taking
advantage of this fact, we can send the differences between the second frame and the first, again
reducing the number of bits required to represent a video signal. Recognizing how this works can enable
one to notice this type of compression when a video signal is close to not working well; when the scene
changes, there is a noticeable lag. This is because the new scene is often very different from the previous
scene, which means the differences between the new frame and the previous frame are many, requiring
more bits, and if those bits are having a hard time getting through, the image will be delayed.
The last type of lossy compression is mathematical, and many, many mathematical algorithms
have been developed for music and video. Many of these take advantage of our understanding of human
perception. For example, we have learned that there are some details in music that, if missing, are not
usually noticeable; removing these details saves bits. The same is true for video – some degradation in
quality is not very noticeable.
Examples of files that have undergone lossy compression include .jpg, .mp3, .mpeg, and
basically all video streamed over the Internet.
6.7.2: Error Detection and Correction (ED&C)
The value of ED&C can be readily perceived. Wouldn’t it be great if the receiver of a signal
could know right away if it had misperceived part of the message? The receiver could then tell the
sender there was a problem, and something could be done to fix the
problem. But how can this be done? First, by taking advantage of the fact
that we’re dealing with digital modulation, so we know there are only
specific values that could be sent. And second, by sending a little extra
(redundant) information about the message. To clarify, consider the
example given in Figure 6.4. In this example, we are restricted to sending
single digits, with values from 0 to 9. Every time we send 4 of these
digits, we follow that 4th digit with a pair of digits, representing the sum
of the previous 4 digits. The transmitter is easily able to calculate this
Figure 6.4: An example
of redundant information,
applied to integer
numbers.
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extra information about the message, and the receiver can readily check the digits as they come across.
If one of the sums doesn’t agree with the received sum of the previous 4 digits, the receiver knows an
error has occurred, and corrective action can be taken.
Parity
The preceding form of error detection is done digitally using a concept known as parity, which is
actually just a binary form of adding. This is shown in Figure 6.5. In these rows, the far right two
columns represent the two types of parity for the previous
8 bits (a bit is either a 0 or a 1). For even parity, the total
number of 1s in each row, including the parity bit, must be
even. For odd parity, the total number of 1s in each row,
including the parity bit, must be odd. So, for the first row,
which contains five 1s, the parity bit must be 1 for even
parity, giving the total row an even number of 1s (six).
The second row has three 1s, so the parity bit must again
be 1, giving the total row an even number of 1s (four).
And in row 3, which has six 1s, the even parity bit must be 0, giving the total row six 1s, again an even
number.
Odd parity can also be used, and this is also shown in Figure 6.5. There is no inherent advantage
to either even or odd parity, but once the decision is made which to use, it is no longer arbitrary for the
receiver to choose even or odd parity – the receiver must choose the same parity as the transmitter.
Looking at Figure 6.5, it is easy to see what would happen if any of the bits were to be
mistakenly reversed by the receiver. The parity for that row would be incorrect, and the receiver would
know an error had occurred. This is also true if one of the parity bits is mistakenly reversed at the
receiver. However, there is a hole in this approach, and it is a rather LARGE hole. If two bits in any row
were to be mistakenly reversed in any given row, the parity would not indicate the presence of an error!
As shown in Figure 6.6, this is also true for any even number of bit errors – they cannot be detected! So,
while parity is easy to implement and detect, it is
not as powerful as we would like it to be – it
misses too many of the cases where multiple bits
have been mistakenly reversed.
Another disadvantage of parity is the
additional (redundant) data that must be
transmitted – the parity bits themselves. For the
example in Figure 6.5, there is one parity bit for every 8 bits, which means 1/9 of the data is redundant –
11.1%. This 11.1% is called overhead. All forms of ED&C require some overhead.
CRC
A second approach to parity, with significantly more detection power, but also with more
complexity, is known as CRC, or Cyclic Redundancy Check. As with the parity error detection
described in the previous paragraph, it also uses binary addition to generate information about the data.
But for CRC, one of the big advantages is that it is able to detect errors involving multiple bits – in fact,
Figure 6.5: Rows of bits and their associated
parity.
Figure 6.6: Bits in error.
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any number of bits in error – within a certain probability, and the probability that an error would be
missed is quite small for 16-bit parity (about 15 parts per million, or ppm). And the overhead is also
quite small – only 16 extra bits need be added, almost irrespective of the size of data file. CRC creates
what is known as a checksum, which is computed using iterative feedback – each new bit causes a
different checksum to be generated. CRC is presently very widely used for error detection in digital
communication. An example of at 16-bit CRC generator is given in Figure 6.7.
For 16-bit CRC, the
number of redundant bits is
always 16, but CRC can be
computed over short blocks
of data or large blocks. If it is
calculated over 100 bits, there
would be 16 redundant bits in 116, or 13.7% overhead, which is on the high side. But if a 16-bit CRC
checksum is calculated over 65,536 bits (4 kbytes), then the overhead drops to only 0.0244% - and that
much lower overhead is great!
But in the end, as good as CRC checksums are, they can only tell that an error has occurred –
they cannot fix the problem. That capability is reserved for the last type of error detection.
FEC
The final type of error detection, known both as Forward Error Correction (FEC) and as Error
Correction Coding (ECC), is much more complicated than the previous two types, and it involves more
overhead and much more computation. But its power is not to be underestimated – it is amazingly
powerful, and has been adapted for use in nearly all forms of digital communication and data storage. Its
power comes from the fact that it goes one major step beyond the previous two types of error detection –
it actually can tell WHICH bit (or bits) were in error. And since we’re dealing with a binary system, as
soon as we know WHICH bit was in error, we also know how to fix it – just change it to the opposite
value!
The math behind practical forms of FEC in use today is fairly complex, but the concept is readily
grasped with an example, as shown in Figures 6.8a & 6.8b. Each row has simple parity added (as
described in the Parity section previously). Likewise, each column also has parity added. While this
results in more overhead, the advantage it gives us is that we can identify WHICH bit was in error in the
block of data.
Knowing this
allows us to fix the
offending bit.
But, as
before, having
multiple bits in
error in the same
row (or column)
causes rather severe
problems for FEC –
Figure 6.7: An example of a 16-bit CRC generator.
Figures 6-8a and 6-8b: A block of data without errors (a), and with errors (b).
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it prevents us from being able to determine which of several bits were actually in error. This could be
fixed with additional parity bits, and this is one of the solutions that has been used. However, even
multiple additional parity bits cannot help us identify all the bad bits if the bad bits are too close
together. And the nature of errors in digital data is that they are almost ALWAYS close together – in
bursts. Whatever the event was that caused one bit to be wrong is also very likely to cause several
adjacent bits (in the same burst) to be wrong. This bursty nature of digital errors (they tend to occur in
bursts) is readily solved by another brilliant yet simple solution: interleaving.
An example of interleaving is given in Figure 6.9. We simply change the order of the bits before
we send them out, so that bits
that were originally adjacent
are not sent adjacent to each
other. Thus, when a burst error
occurs, it does NOT affect
originally adjacent bits. In the
example of Figure 6.9, a burst
error 8 bits in length would
wipe out bits in 8 different
bytes of the 64-bit stream, but none of these bytes would have more than 1 bit in error, which is easy to
detect and correct. Fortunately, the hardware required to implement interleaving is very simple and
efficient, and this innovation allows us to use less complicated FEC codes, and reduces the necessary
overhead.
The power of FEC is best grasped with an example. FEC of a type known as Reed-Solomon is
widely used in optical disc storage (and MANY other applications). In the case of DVDs, it requires
approximately 25% overhead (meaning that of every 100 bits, approximately 25 of them are FEC bits).
In reading back the data from a DVD, an error typically occurs once in every 200 bits. This may not
sound bad, but keeping in mind that the data rate we’re dealing with here is 11 Mbps (11 million bits per
second), this means we would typically experience 55,000 errors every second! Clearly, this is an
unacceptable error rate. But with the 25% FEC bits added in, the playback circuits can actually detect
and correct these errors, improving the actual error rate by approximately 18 orders of magnitude! Thus,
instead of experiencing an average of 55,000 errors each second, we are able to reduce this to only
experiencing an average of one error every 50,000 years!
6.8 Networking: The Backbone of Computer Communication As the title of this section states, networking is the backbone of communication between
computers today, and for the foreseeable future. In its simplest sense, a network is three or more
computers which communicate with each other; in a more complex sense, it is multiple clusters of
computers which communicate within each cluster and with other clusters of computers. This more
complex sense of networking is essentially what the Internet is; more on that in the next section.
There are several terms which are unique in networking, so we will need to understand them
first. One of these terms is packet. A packet is a collection of bits associated with each other and which
have a specific order in which the bits are transmitted. Figure 6.10 gives an example of the typical
Figure 6-9: An example of interleaving 8 bytes.
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anatomy of a packet. The payload
can be fixed or variable, but
generally a message to be sent from
A to B will involve multiple packets.
Each packet is independent of all others, and all packets can take different routes to get from A to B.
The Internet is a network of networks, allowing computers anywhere in the world to connect to
any other computer in the world. There are many standards in place that make this possible; this section
will discuss some of these standards.
A protocol is a formal agreement (can also be a standard) by which communication takes place.
It covers all the necessary topics that need to be addressed, and is often known by its acronym. An
example is TCP/IP, which stands for Transmission Control Protocol/Internet Protocol, two of the main
protocols governing Internet communication.
A frame is very much like a packet, but at a higher level of encapsulation in the OSI model of
computer networking. This encapsulation is exemplified in Figure 6.11. At the lowest layer, we have
data which is sent over
some physical media
(wire, wireless, or optical
fiber) in the form of a
voltage variation with
respect to time; also
included in the Physical
layer are coding and
framing, which are not
covered in this chapter,
but which group together
these voltage variations
into groups of bits. At the
next layer, these bits are
compiled into an Ethernet
packet (the payload), with an appropriate header and checksum as shown in Figure 6.10. At the Network
layer, the Ethernet packet becomes the IP payload, which then gets an IP header added. And at the
Transport layer, the IP payload and header become the TCP payload, which then gets the appropriate
TCP header added. The TCP packet is now ready for transmission over the Internet.
A router is basically a computer which is dedicated to receiving packets, deciding the best way
to get each packet one step closer to its final destination, then sending each packet to that next router.
With enough routers (and there are millions), each packet eventually makes its way to its final
destination.
Latency is a measure of the time it takes a packet to transport from A to B. Latency is composed
of three parameters: transmission time (the physical time it takes am EM signal to traverse the distance
from A to B), the number of hops (routers) it encounters along the way, and the time it takes each router
to forward the packet to the next destination. For packets remaining on this planet, latency is dominated
by the latter two parameters, since distance is small compared to the speed of EM waves.
Figure 6.10: The anatomy of a typical packet.
Figure 6.11: Encapsulation in the 7-layer OSI model of the Internet.
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Jitter is the variation in latency, and is very important for time-sensitive signals such as
streaming music or video. Because each packet is sent independently, they can all take different routes
getting from A to B. Since latency is dominated by the number of hops and the time each hop takes, it is
common for packets to arrive out of order. This requires that B buffer the packets until the packets can
be put back in the right order. Thus, the larger the jitter, the larger the buffers at B must be, and the
longer the delay from when A starts sending to when B can start presenting what is being sent.
Packet loss ratio (PLR) is a measure of the percentage of packets that are lost along the way
from A to B. Because routers engage in what is called a best-effort protocol (delivery is not guaranteed,
but generally works), some packets don’t make it all the way from A to B. This can be due to congestion
in the Internet, to noisy links, or to the presence of higher-priority traffic, but it is always undesirable.
PLRs below 2% are generally tolerable for most Internet traffic.
Networking has, historically, been designed around this probabilistic protocol – there is a high
probability of knowing when your packet will make it from A to B, and how likely it is that it will make
it. There are other protocols which guarantee delivery (PLR = 0.0%) and have a fixed latency (jitter = 0),
but they have not come to dominate due to cost reasons, and due to the remarkable flexibility of
networking equipment built to tolerate this probabilistic packet delivery system.
6.9 The Internet: History of a Modern Marvel The Internet has truly become as integral a part of our society as automobiles, highways,
electricity, and telephones. It would set our modern civilization back quickly and severely if the Internet
were to suddenly disappear.
Perhaps one of the first things we should do is clarify what is meant by “internet” and “the
Internet”, for these terms have grown to mean two different things. An “internet” is simply a network of
computers which are connected to each other so that they can share data. As useful as this is, it pales in
comparison to the usefulness of “the Internet”, which means the world-wide interconnection of
computers. The Internet interconnects everyone with access to it – users can send and receive
information from any other Internet user, or from any of the hundreds of millions of websites that are
out there.
A saying about the Internet is attributed to Robert Metcalfe: “The value of a telecommunications
network is proportional to the square of the number of connected users of the system.” While the exact
quantification of the value of a telecommunications network is certainly subject to debate, no one can
argue against the basic premise: the value of the Internet has increased as a function of the number of
people connected to it. First begun in the 1960s as a way to interconnect computers working on
ARPANET, the number of computers connected to the Internet grew only slowly, and relatively few
people in the world knew or cared about it. But with the introduction of a point-and-click interface (also
known as a graphical user interface or GUI) in the early 1990s (also known as a web browser), coupled
with the increase in home computing, its usefulness began to grow rapidly. And as it grew, its value
increased greatly, so that in only a few years it became almost essential. Today, a computer isn’t even
considered fully a computer unless it has access to the Internet and the vast amount of information
available through it.
At its core, the Internet consists of a network interface circuit built into each computer, along
with routers and data centers distributed throughout the world. Computers today interface to the Internet
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through two main standards: WiFi (also known as IEEE 802-11) and Ethernet. WiFi is the wireless
access, highly convenient for mobile computing. Ethernet is the wired standard, giving high
performance (high data rates) and somewhat more security than wireless access.
Routers were discussed in the previous section, and they are an integral part of the Internet.
Between routers are various connection standards, some for low cost (and usually low data rates and/or
short distances), and others for very high data rates and/or long distances (and usually high cost). Some
of these connection
standards are show
in Table 6.6. An
example of a router
is shown in Figure 6-
12.
Data centers
are truly one of the
marvels of the
modern Internet.
They come in many
sizes, from very small to huge.
Google is one of the few companies
which has released public
information on their data centers. At
last count, they had 15 data centers, 8
in the USA, 4 in Europe, 2 in Asia,
and 1 in Chile. They have over
2,000,000 servers (computers
dedicated to providing files and other
data to querying customers). Figure 6.13 shows some of their pictures of their data centers. Data centers
consist of rows and rows of racks of servers and HDDs (hard-disk drives), along with associated
plumbing to remove the heat produced by all the hardware, and cables to connect everything to the
Internet. They are very expensive to build (large ones like these can be upwards of $700 M) and very
expensive to operate (they require about 30 MW of power, continuously, which works out to about
$100,000/month), in addition to requiring continual maintenance and backups for everything.
Table 6.6: Some of the standards that connect computers together over the Internet.
Figure 6-12: An example of a router.
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6.10 Wireless: The Ultimate in Connectivity Convenience When it comes to mobility, nothing beats the convenience of wireless access. However, of the
three media for transmitting data, wireless tends to be the most problematic, which is why it has taken
decades to develop protocols and standards capable of delivering the performance we tend to expect.
Table 6.7 summarizes some of the most common wireless standards in use today. It is expected that
more standards
will be
developed, as a
great deal of
work is going on
in the field of
wireless
technologies
today.
Significant
improvements
are regularly
being made in
hardware and
software, and the
public demand
for, and
appreciation of,
these
technologies
continues to
grow.
6.11 Automation Standards: Performance and Convenience Over the past several decades, many automation standard have been proposed, implemented, and
disappeared. Since none is ever a perfect solution, efforts have continued at improving these standards,
and this is sure to continue. Table 6.8 summarizes some of the more popular industrial automation
communication standards in use today.
Table 6.7: Examples of some common wireless standards in use today, and their respective
characteristics.
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Summary
Modern electronic
communication, over any
of the common media, has
grown in popularity and
performance for several
decades. There are many
options available today,
with continual
improvements in nearly all
areas. The future is bound
to provide us even more
impressive solutions as the
progress continues.
Figure 6.13: Pictures from Google of the insides of some of their data centers.
Table 6.8: Industrial automation standards in use today and their respective
characteristics.
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Problems 1. Choose one thing about the Voyager 1 and 2 deep space probes that you find the most interesting, and explain why you chose it. (5 points) 2. Figure 6.1 shows the EM spectrum. It seems to convey that there is an unlimited amount of EM spectrum available to us for data communication, but this is not the case. What is the main reason this is not the case? (5 points) 3. What are the three basic types of modulation available to us? (5 points)
4. Explain why Shannon’s Law is one of the most important and most fundamental laws governing digital
communication. (5 points)
5. Wire media has been used for digital communication since the early days of Morse code, clear back in the
1860’s. Explain why such an incredibly old media has not been replaced by wireless or optical fiber. (5 points)
6. What are the two factors that must be considered when converting analog signals to digital signals? (5 points)
7. According to the Nyquist criterion, what is the highest frequency signal that can be adequately converted to
digital if sampling at a rate of 150 ksamples/sec? (5 points)
8. What is the step size (quantization error) of a signal of 85 kHz, a magnitude of 15 Vp-p, a phase of 0°, and
which is being converted to a digital signal using samples of 12 bits? (5 points)
9. Assume you want to send a signal from A to B, and must compress it before sending it. How would you choose
the type of compression you would use, whether lossy or lossless? (5 points)
10. Give one advantage and one disadvantage of CRC (cyclic redundancy checking). (5 points)
11. Give one advantage and one disadvantage of FEC (forward error correction). (5 points)
12. Explain why interleaving is always done when doing FEC. (5 points)
13. Explain why a packet sequence number (see Figure 6.10) is necessary. (5 points)
14. Many historians claim that the invention of the Internet, together with the World-Wide Web, constitute one of
the major wonders of the modern technical world. Explain why such a claim is quite reasonable. (5 points)
15. Explain why there are so many different wireless and industrial automation standards. (5 points)