Chapter4 digital transmission

Chapter 4
Digital Transmission

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Digital TransmissionDigital Transmission
Conversion
methods
Digital/Digital
encoding
Analog/Digit
al
encoding
Digital/Analog
encoding
Analog/Anal
og
encoding
Polar BipolarUnipolar DMPCM ASK FSK PSK
QAM
AM FM PM
 The Information needs to be converted to either a digital
signal or an analog signal for transmission
MultitransitionMultilevel

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4.2 Block Coding4.2 Block Coding
We need redundancy to endure synchronization
and to provide some kind of inherent error
detecting.
Block coding can give us redundancy to endure
Synchronization and improve the performance of
line coding.
Block coding is normally referred to as
mB/nB coding;
it replaces each m-bit group with an
n-bit group.

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 The slash in block encoding (for example, 4B/5B)
distinguishes block encoding from multilevel encoding
(for example, 8B6T), which is written without a slash.

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Block Coding (cont’d)Block Coding (cont’d)
 Steps in transmission
Step 1: Division
divide sequence of bits into groups of m bits
Step 2: Substitution
substitute an m-bit code for an n-bit group
The heart of block coding is the substitution
step.
For example, in 4B/5B encoding we substitute
a 4-bit code for a 5-bit group.
 Step 3: Combination
•N bit groups are combined together to form a stream.
The new stream has more bits than the original bits.

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Figure 4.14 Block coding concept

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4B/5B4B/5B
 The four binary/five binary (4B/5B) coding scheme was designed to be
used in combination with NRZ-I.
 Recall that NRZ-I has a good signal rate, one-half that of the biphase, but it
has a synchronization problem.
 A long sequence of 0s can make the receiver clock lose synchronization.
 One solution is to change the bit stream, prior to encoding with NRZ-I, so
that it does not have a long stream of 0s.
 The 4B/5B scheme achieves this goal.
 The block-coded stream does not have more that three consecutive 0s, as
we will see later. At the receiver, the NRZ-I encoded digital signal is first
decoded into a stream of bits and then decoded to remove the
redundancy.

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Figure 4.15 Using block coding 4B/5B with NRZ-I line coding scheme

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Figure 4.16 Substitution in 4B/5B block coding

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Table 4.2 4B/5B mapping codes

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 In 4B/5B, the 5-bit output that replaces the 4-bit input has no
more than one leading zero (left bit) and no more than two trailing
zeros (right bits).
 So when different groups are combined to make a new sequence,
there
are never more than three consecutive 0s.
 (Note that NRZ-I has no problem with sequences of Is.)
 Table 4.2 shows the corresponding pairs used in 4B/5B encoding.
 Note that the first two columns pair a 4-bit group with a 5-bit
group.
 A group of 4 bits can have only 16 different combinations while a
group
of 5 bits can have 32 different combinations.

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 Some of these unused groups are used for control
purposes;
the others are not used at all.
 The latter provide a kind of error detection.
 If a 5-bit group arrives that belongs to the unused
portion of
the table, the receiver knows that there is an error in the
transmission.

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 Figure 4.16 shows an example of substitution in 4B/5B
coding.
 4B/5B encoding solves the problem of synchronization and
overcomes one of the deficiencies of NRZ-1.
 However, we need to remember that it increases the signal
rate of NRZ-1.
 The redundant bits add 20 percent more baud.
 Still, the result is less than the biphase scheme which has a
signal rate of 2 times that of NRZ-1. does not solve the DC
component .
 However, 4B/5B block encoding problem of NRZ-1.
 If a DC component is unacceptable, we need to use

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Example 4.5Example 4.5
 We need to send data at a 1-Mbps rate.
 What is the minimum required bandwidth, using a
combination of 4B/5B and NRZ-I or Manchester coding?
 First 4B/5B block coding increases the bit rate to 1.25
Mbps.
 The minimum bandwidth using NRZ-I is NI2 or 625 kHz.
 The Manchester scheme needs a minimum bandwidth of
1 MHz
 The first choice needs a lower bandwidth, but has a DC
component problem;
 the second choice needs a higher bandwidth, but does
not

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8B/10B8B/10B
 The eight binary/ten binary (8B/10B) encoding is similar to
4B/5B
encoding except that a group of 8 bits of data is now substituted
by a
10-bit code.
 It provides greater error detection capability than 4B/5B.
 The 8B/10B block coding is actually a combination of 5B/6B and
3B/4B encoding, as shown in Figure 4.17.
 The most five significant bits of a 10-bit block is fed into the
5B/6B encoder; the least 3 significant bits is fed into a 3B/4B
encoder.
 The split is done to simplify the mapping table.

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 To prevent a long run of consecutive Os or Is, the code
uses a disparity controller which keeps track of excess Os
over Is
(or Is over Os).
 If the bits in the current block create a disparity that
contributes to the previous disparity (either direction),
then each bit in the
code is complemented (a 0 is changed to a 1 and a 1 is
changed to a 0).
 The coding has 210 - 28 =768 redundant groups that can
be
used for disparity checking and error detection.
 In general, the technique is superior to 4B/5B because of

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Figure 4.17 8B/10B block encoding

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ScramblingScrambling
 Biphase suitable for dedicated links between stations in LAN
are not suitable for long-distance communication because of
their wide bandwidth requirement and DC component.
 The combination of block coding and NRZ line coding is not suitable for
long-distance encoding either, because of the DC component.
 Bipolar AMI encoding, on the other hand, has a narrow bandwidth and does
not create a DC component.
 However, a long sequence of Os upsets the synchronization.
 If we can find a way to avoid a long sequence of Os in the original stream,
we can use bipolar AMI for long distances.
 We are looking for a technique that does not increase the number of bits
and does provide synchronization.

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 We are looking for a solution that substitutes long zero-
level pulses with a combination of other levels to
provide synchronization. One solution is called
scrambling.
 We modify part of the AMI rule to include scrambling, as
shown in
Figure 4.18.
 Note that scrambling, as opposed to block coding, is
done at
the same time as encoding.
 The system needs to insert the required pulses based
on the
defined scrambling rules.

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Scrambling (contScrambling (cont’’d)d)
Figure 4.18 AMI used with scrambling

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B8ZSB8ZS
 Bipolar with 8-zero substitution (BSZS) is commonly used in
North America.
 In this technique, eight consecutive zero-level voltages are
replaced by the sequence OOOVBOVB.
 The V in the sequence denotes violation; this is a nonzero
voltage
that breaks an AMI rule of encoding (opposite polarity from
the previous).
 The B in the sequence denotes bipolar; which means a
nonzero level voltage in accordance with the AMI rule.
 There are two cases, as shown in Figure 4.19.

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 Note that the scrambling in this case does not change the
bit rate.
 Also, the technique balances the positive and negative
voltage
levels (two positives and two negatives), which means that
the DC balance is maintained.
 Note that the substitution may change the polarity of a 1
because, after the substitution, AMI needs to follow its
rules.
 The letter V (Violation) or B (bipolar) here is relative.
 The V means the same polarity as the polarity of the
precious nonzero pulse; B means the polarity opposite to
the polarity of the previous non zero pulse.

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Figure 4.19 Two cases of B8ZS scrambling technique
B8ZS substitutes eight consecutive
zeros with 000VB0VB.

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HDB3HDB3
 High-density bipolar 3-zero (HDB3) is commonly used
outside of
North America.
 In this technique, which is more conservative than B8ZS, four
consecutive zero-level voltages are replaced with a
sequence of
OOOV or BOOV: The reason for two different substitutions
is to maintain the even number of nonzero pulses after each
substitution.
The two rules can be stated as follows:

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 1. If the number of nonzero pulses after the last
substitution
is odd, the substitution pattern will be OOOV, which
makes
the total number of nonzero pulses even.
 2. If the number of nonzero pulses after the last
substitution
is even, the substitution pattern will be BOOV, which
makes
the total number of nonzero pulses even.

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Figure 4.20 Different situations in HDB3 scrambling technique
HDB3 substitutes four consecutive zeros with
000V or B00V depending on the number of
nonzero pulses after the last substitution.

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 There are several points we need to mention here.
 First, before the first substitution, the number of
nonzero
pulses is even, so the first substitution is B00V.
 After this substitution, the polarity of the 1 bit is
changed
because the AMI scheme, after each substitution, must
follow its own rule.
 After this bit, we need another substitution, which is
OOOV
because we have only one nonzero pulse (odd) after
the last
substitution.

4.2 ANALOG-TO-DIGITAL CONVERSION4.2 ANALOG-TO-DIGITAL CONVERSION
We have seen in Chapter 3 that a digital signal isWe have seen in Chapter 3 that a digital signal is
superior to an analog signal.superior to an analog signal.
Analog signal comes from microphone or camera. TheAnalog signal comes from microphone or camera. The
tendency today is to change an analog signal to digitaltendency today is to change an analog signal to digital
data. In this section we describe two techniques,data. In this section we describe two techniques, pulsepulse
code modulationcode modulation andand delta modulationdelta modulation..
After the digital data are created , we can use one ofAfter the digital data are created , we can use one of
these techniques to convert the digital data to a digitalthese techniques to convert the digital data to a digital
signal using the coding schemes specified in 4.1signal using the coding schemes specified in 4.1
Pulse Code Modulation (PCM)
Delta Modulation (DM)
Topics discussed in this section:Topics discussed in this section:

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Pulse Code Modulation (PCM)Pulse Code Modulation (PCM)
 Most common technique to change an analog signal to
digital data (digitization) is called Pulse Code Modulation
(PCM). PCM encoder has 3 processes.
Figure 4.21 Components of PCM encoder

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1. Analog Signal is Sampled
2. Sampled signal is Quantized
3. The Quantized values are encoded as stream of bits

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SamplingSampling
 The first step in PCM is sampling.
 The analog signal is sampled every Ts S, where Ts is the sample interval or
period.
 The inverse of the sampling interval is called the sampling rate or
sampling frequency and denoted by fs, where fs = 1/Ts‘
 There are three sampling methods-ideal, natural, and flat-top-as.
•Term sampling means measuring the amplitude of the signal
at equal intervals.

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Sampling (contSampling (cont’’d)d)
Figure 4.22 Three different sampling methods for PCM

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 In ideal sampling, pulses from the analog signal are sampled.
 This is an ideal sampling method and cannot be easily
implemented.
 In natural sampling, a high-speed switch is turned on for only
the small period of time when the sampling occurs.
 The result is a sequence of samples that retains the shape of the
analog signal.
 The most common sampling method, called sample and hold,
however, creates flat-top samples by using a circuit.
 The sampling process is sometimes referred to as pulse
amplitude
modulation (PAM).
 We need to remember, however, that the result is still an analog
signal with nonintegral values.

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Sampling RateSampling Rate
 One important consideration is the sampling rate or
frequency.
What are the restrictions on Ts?
This question was elegantly answered by Nyquist.
According to the Nyquist theorem, to reproduce the original
analog signal, one necessary condition is that the sampling
rate
be at least twice the highest frequency in the original signal.

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According to the Nyquist theorem, the
sampling rate must be
at least 2 times the highest frequency
contained in the signal.
Note
Restriction on Ts
To Reproduce the Original analog Signal

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 We need to elaborate on the theorem at this point.
 First, we can sample a signal only if the signal is band-
limited
 In other words, a signal with an infinite bandwidth
cannot be
sampled.
 Second, the sampling rate must be at least 2 times the
highest frequency, not the bandwidth.
 If the analog signal is low-pass, the bandwidth and the
highest frequency are the same value.
 If the analog signal is bandpass, the bandwidth value is
lower than the value of the maximum frequency.
 Figure 4.23 shows the value of the sampling rate for

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Figure 4.23 Nyquist sampling rate for low-pass and bandpass signals

For an intuitive example of the Nyquist theorem, let us
sample a simple sine wave at three sampling rates: fs = 4f
(2 times the Nyquist rate), fs = 2f (Nyquist rate), and
fs = f (one-half the Nyquist rate). Figure 4.24 shows the
sampling and the subsequent recovery of the signal.
It can be seen that sampling at the Nyquist rate can create
a good approximation of the original sine wave (part a).
Oversampling in part b can also create the same
approximation, but it is redundant and unnecessary.
Sampling below the Nyquist rate (part c) does not produce
a signal that looks like the original sine wave.
Example 4.6
Sampling (cont’d)Sampling (cont’d)

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Figure 4.24 Recovery of a sampled sine wave for different sampling rates

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Consider the revolution of a hand of a clock. The second
hand of a clock has a period of 60 s. According to the
Nyquist theorem, we need to sample the hand every 30 s
(Ts = T or fs = 2f ). In Figure 4.25a, the sample points, in
order, are 12, 6, 12, 6, 12, and 6. The receiver of the
samples cannot tell if the clock is moving forward or
backward. In part b, we sample at double the Nyquist rate
(every 15 s). The sample points are 12, 3, 6, 9, and 12.
The clock is moving forward. In part c, we sample below
the Nyquist rate (Ts = T or fs = f ). The sample points are
12, 9, 6, 3, and 12. Although the clock is moving forward,
the receiver thinks that the clock is moving backward.
Example 4.7

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Figure 4.25 Sampling of a clock with only one hand

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An example related to Example 4.7 is the seemingly
backward rotation of the wheels of a forward-moving car
in a movie. This can be explained by under-sampling. A
movie is filmed at 24 frames per second. If a wheel is
rotating more than 12 times per second, the under-
sampling creates the impression of a backward rotation.
Example 4.8

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Telephone companies digitize voice by assuming a
maximum frequency of 4000 Hz. The sampling rate
therefore is 8000 samples per second.
Example 4.9

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A complex low-pass signal has a bandwidth of 200 kHz.
What is the minimum sampling rate for this signal?
Solution
The bandwidth of a low-pass signal is between 0 and f,
where f is the maximum frequency in the signal.
Therefore, we can sample this signal at 2 times the
highest frequency (200 kHz). The sampling rate is
therefore 400,000 samples per second.
Example 4.10

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A complex bandpass signal has a bandwidth of 200 kHz.
What is the minimum sampling rate for this signal?
Solution
We cannot find the minimum sampling rate in this case
because we do not know where the bandwidth starts or
ends. We do not know the maximum frequency in the
signal.
Example 4.11

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QuantizationQuantization
 The result of sampling is a series of pulses with amplitude values
between the max. and min. amplitudes of the signal.
 These values cannot be used in the encoding process.
 The following are the steps in quantization:
Assume the original analog signal has instantaneous amplitudes
between Vmin. and Vmax.
Divide the range into L zones, each of height Δ (delta)
Δ = (Vmin. - Vmax.) / L
Assign quantized values of 0 to L-1 to the midpoint of each zone
Approximate the value of the sample amplitude to the quantized values.
Example: sampled signal and the sample amplitude between -20 and
+20V. We decide to have eight levels (L=8). This means ∆=5V. Fig shows
this example.

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Quantization (contQuantization (cont’’d)d)
Figure 4.26 Quantization and encoding of a sampled signal
ACTUAL
AMPLITUTDE/Δ
Middle of Zone
Middle of
Zone
Row1 – Row2
Quantized levels at left
Quantized levels at left

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What is the SNRdB in the example of Figure 4.26?
Solution
We can use the formula to find the quantization. We have
eight levels and 3 bits per sample, so
SNRdB = 6.02(3) + 1.76 = 19.82 dB
Increasing the number of levels increases the SNR.
Example 4.12

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 We have shown only nine samples using ideal sampling
(for
simplicity). The value at the top of each sample in the
graph
shows the actual amplitude.
 In the chart, the first row is the normalized value for
each
sample (actual amplitude/∆).
 The quantization process selects the quantization value
from
the middle of each zone.
 This means that the normalized quantized values
(second row) are different from the normalized
amplitudes.

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Quantization LevelsQuantization Levels
 In the previous example, we showed eight quantization
levels.
 The choice of L, the number of levels, depends on the
range of
the amplitudes of the analog signal and how accurately
we need to recover the signal.
 If the amplitude of a signal fluctuates between two values
only, we need only two levels; if the signal, like voice,
has many
amplitude values, we need more quantization levels.
 In audio digitizing, L is normally chosen to be 256;
 in video it is normally thousands.

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Quantization ErrorQuantization Error
 One important issue is the error created in the quantization
process. (Later, we will see how this affects high-speed
modems.) Quantization is an approximation process.
 The input values to the quantizer are the real values;
 the output values are the approximated values.
 The output values are chosen to be the middle value in the
zone.
 If the input value is also at the middle of the zone,
there is no quantization error;
otherwise, there is an error.

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 In the previous example, the normalizedamplitude of
the third sample is 3.24, but the normalized quantized
value is 3.50.
 This means that there is an error of +0.26.
 The value of the error for any sample is less than
△/2 .
 In other words, we have -△/2≤error ≤ △/2.

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 The quantization error changes the signal-to-noise ratio
of the signal, which in turn reduces the upper limit
capacity
according to Shannon.
 It can be proven that the contribution of the quantization
error to the SNRdB of the signal depends on the
number of
Quantization levels L, or the bits per sample nb' as shown
in the
following formula:
 Quantization Error
SNRdB = 6.02nb + 1.76 dB

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What is the SNRdB in the example of Figure 4.26?
Solution
We can use the formula to find the quantization. We have
eight levels and 3 bits per sample, so
SNRdB = 6.02(3) + 1.76 = 19.82 dB
Increasing the number of levels increases the SNR.
Example 4.12

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A telephone subscriber line must have an SNRdB above
40. What is the minimum number of bits per sample?
Solution
We can calculate the number of bits as
Example 4.13
Telephone companies usually assign 7 or 8 bits per
sample.

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We want to digitize the human voice. What is the bit rate,
assuming 8 bits per sample?
Solution
The human voice normally contains frequencies from 0
to 4000 Hz. So the sampling rate and bit rate are
calculated as follows:
Example 4.14

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Figure 4.27 Components of a PCM decoder

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We have a low-pass analog signal of 4 kHz. If we send the
analog signal, we need a channel with a minimum
bandwidth of 4 kHz. If we digitize the signal and send 8
bits per sample, we need a channel with a minimum
bandwidth of 8 × 4 kHz = 32 kHz.
Example 4.15

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A telephone subscriber line must have an SNRdB above
40. What is the minimum number of bits per sample?
Solution
We can calculate the number of bits as
Example 4.13
Telephone companies usually assign 7 or 8 bits per
sample.

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Uniform Vs. Non uniform QuantizationUniform Vs. Non uniform Quantization
 For many applications, the distribution of the instantaneous
amplitudes in the analog signal is not uniform.
 Changes in amplitude often occur more frequently in the
lower amplitudes than in the higher ones.
 For these types of applications it is better to use
nonuniform
zones.
 In other words, the height of is not fixed; it is greater near
the
Lower amplitudes and less near the higher amplitudes.
 Nonuniform quantization can also be achieved by using a
process called companding and expanding.

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 The signal is companded at the sender before
conversion; it
is expanded at the receiver after conversion.
 Companding means reducing the instantaneous voltage
amplitude for large values; expanding is the opposite
process.
 Companding gives greater weight to strong signals and
less weight to weak ones.
 It has been proved that nonuniform quantization
effectively
reduces the SNRdB of quantization

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EncodingEncoding
 The last step in PCM is encoding.
 After each sample is quantized and the number of bits per
sample is decided, each sample can be changed to an nb-bit
code word.
 A quantization code of 2 is encoded as 010; 5 is
encoded as
101; and so on.
 Note that the number of bits for each sample is
determined
from the number of quantization levels.
 If the number of quantization levels is L, the number of
bits

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 . In our example L is 8 and nb is therefore 3. The bit rate
can
be found from the formula
Bit rate = sampling rate x number of bits per sample = fs x nb
where No. of quantization level : L , No. of bits (nb )= log2 L

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Encoding (contEncoding (cont’’d)d)
We want to digitize the human voice. What is the bit rate,
assuming 8 bits per sample?
Solution
The human voice normally contains frequencies from 0
to 4000 Hz. So the sampling rate and bit rate are
calculated as follows:
Example 4.14

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Original Signal RecoveryOriginal Signal Recovery
 The recovery of the original signal requires the PCM
decoder.
 The decoder first uses convert the code words into a
pulse
that holds the amplitude until the next pulse.
 After the staircase signal is completed, it is passed
through a low-pass filter to smooth the staircase signal
into an analog
signal.
 The filter has the same cutoff frequency as the original
signal at the sender.
 If the signal has been sampled at (or greater than) the
Nyquist sampling rate and if there are enough

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 The original signal will be recreated.
 Note that the maximum and minimum values of the
original signal can be achieved by using amplification.
 Figure 4.27 shows the simplified process.

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Original Signal RecoveryOriginal Signal Recovery
Figure 4.27 Components of a PCM decoder

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PCM BandwidthPCM Bandwidth
 If we digitized the signal, what is the new bandwidth of the
channel ?
Bmin = c x N x 1/r = c x nb xfs x 1/r = c x nb x 2 Banalog x 1/r
 The minimum bandwidth
Bmin = nb x Banalog
 The maximum data rate of a Channel
Nmax = 2 x B x log 2 L (bps)
 The minimum bandwidth
Bmin = N / (2 x log 2 L) (Hz)

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PCM BandwidthPCM Bandwidth
We have a low-pass analog signal of 4 kHz. If we send the
analog signal, we need a channel with a minimum
bandwidth of 4 kHz. If we digitize the signal and send 8
bits per sample, we need a channel with a minimum
bandwidth of 8 × 4 kHz = 32 kHz.
Example 4.15

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Delta ModulationDelta Modulation
 Delta Modulation (DM) techniques have been developed to
reduce the complexity of PCM.
 PCM finds the value of the signal amplitude for each sample;
DM finds the change from the previous sample.
Figure 4.28 The process of delta modulation

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Delta Modulation (contDelta Modulation (cont’’d)d)
Figure 4.29 Delta modulation components

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Delta Modulation (contDelta Modulation (cont’’d)d)
Figure 4.30 Delta demodulation components

4.3 TRANSMISSION MODES4.3 TRANSMISSION MODES
The transmission of binary data across a link can beThe transmission of binary data across a link can be
accomplished in either parallel or serial mode. Inaccomplished in either parallel or serial mode. In
parallel mode, multiple bits are sent with each clockparallel mode, multiple bits are sent with each clock
tick. In serial mode, 1 bit is sent with each clock tick.tick. In serial mode, 1 bit is sent with each clock tick.
While there is only one way to send parallel data, thereWhile there is only one way to send parallel data, there
are three subclasses of serial transmission:are three subclasses of serial transmission:
asynchronous, synchronous, and isochronous.asynchronous, synchronous, and isochronous.
Parallel Transmission
Serial Transmission
Topics discussed in this section:Topics discussed in this section:

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Transmission ModesTransmission Modes
Figure 4.31 Data transmission and modes

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Transmission Modes (contTransmission Modes (cont’’d)d)
Figure 4.32 Parallel transmission

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Figure 4.33 Serial transmission

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In asynchronous transmission, we send
1 start bit (0) at the beginning and 1 or
more stop bits (1s) at the end of each
byte. There may be a gap between
each byte.
Asynchronous here means
“asynchronous at the byte level,”
but the bits are still synchronized;
their durations are the same.

7979
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Figure 4.34 Asynchronous transmission

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Kyung Hee
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In synchronous transmission, we send
bits one after another without start or
stop bits or gaps. It is the responsibility
of the receiver to group the bits.

8181
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University
Figure 4.35 Synchronous transmission

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Kyung Hee
University
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Chapter4 digital transmission

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Chapter4 digital transmission