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Digital Transmission
Digital to Digital Transmission
A computer network is designed to send information from one point to another. This information
needs to be converted to either a digital signal or an analog signal for transmission. Techniques for
conversion digital and analog data to digital signal, commonly referred to as encoding techniques.
The digital to digital
conversion involves three techniques: line coding, block coding, and
scrambling. Line coding is always needed block coding and scrambling mayor may not be needed.
Line Coding
Line coding is the process of converting digital data to digital signals. Assume that data, in the form
of text, numbers, graphical images, audio, or video, are stored in computer memory as sequences of
bits . Line coding converts a sequence of bits to a digital signal. At the sender, digital data are
encoded into a digital signal; at the receiver, the digital data are recreated by decoding the digital
signal.
Characteristics
Signal Element Versus Data Element : A data element is the smallest entity that can represent a
piece of information: this is the bit. In digital data communications, a signal element carries data
elements. A signal element is the shortest unit (timewise) of a digital signal. In other words, data
elements are what we need to send; signal elements are what we can send. Data elements are
being carried; signal elements are the carriers.
We define a ratio r which is the number of data elements carried by each signal element. Figure
shows several situations with different values of r.
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Suppose each data element IS a person who needs to be carried from one place to another.
We can think of a signal element as a vehicle that can carry people. When r = 1, it means each
person is driving a vehicle. When r > 1, it means more than one person is travelling in a vehicle (a
carpool, for example). We can also have the case where one person is driving a car and a trailer (r =
1/2 ).
Data Rate Versus Signal Rate : The data rate defines the number of data elements (bits) sent in one
second. The unit is bits per second (bps). The signal rate is the number of signal elements sent in one
second. The unit is the baud. The data rate is sometimes called the bit rate; the signal rate is
sometimes called the pulse rate, the modulation rate, or the baud rate. One goal in data
communications is to increase the data rate while decreasing the signal rate. Increasing the data rate
increases the speed of transmission; decreasing the signal rate decreases the bandwidth requirement.
In our vehicle-people analogy, we need to carry more people in fewer vehicles to prevent
traffic jams. We have a limited bandwidth in our transportation system.
We now need to consider the relationship between data rate and signal rate (bit rate and baud rate).
This relationship, of course, depends on the value of r. It also depends on the data pattern. If we have
a data pattern of all 1s or all 0s, the signal rate may be different from a data pattern of alternating 0s
and Is. To derive a formula for the relationship, we need to define three cases: the worst, best, and
average. The worst case is when we need the maximum signal rate; the best case is when we need
the minimum. In data communications, we are usually interested in the average case. We can
formulate the relationship between data rate and signal rate as
S =c * N * (1 /r)baud
where N is the data rate (bps); c is the case factor, which varies for each case; S is the
number of signal elements; and r is the previously defined factor.
However, most digital signals we encounter in real life have a bandwidth with finite values. In other
words, the bandwidth is theoretically infinite, but many of the components have such a small
amplitude that they can be ignored. The effective bandwidth is finite. We can say that the baud rate,
not the bit rate, determines the required bandwidth for a digital signal. The minimum bandwidth can
be given as
Bmin = c * N * 1/r
We can solve for the maximum data rate if the bandwidth of the channel is given.
N max = 1/c * B *r
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No of signal levels L: This refers to the number values allowed in a signal, known as signal levels,
to represent data. A signal with L levels actually can carry log2 L bits per level. If each level
corresponds to one signal element and we assume the average case (c = 1/2), then we have
DC Components : After line coding, the signal may have zero frequency component in the spectrum
of the signal, which is known as the direct-current (DC) component. DC component in a signal is
not desirable because the DC component does not pass through some components of a
communication system such as a transformer. This leads to distortion of the signal and may create
error at the output. The DC component also results in unwanted energy loss on the line.
So a good line coding scheme should not have DC components.
Self-synchronization : To interpret the received signals correctly, the bit intervals of the receiver
should be exactly same or within certain limit of that of the transmitter. If the receiver clock is faster
or slower, the bit intervals are not matched and the receiver might misinterpret the signals. Usually,
clock is generated and synchronized from the received signal with the help of a special hardware
known as Phase Lock Loop (PLL). However, this can be achieved if the received signal is selfsynchronizing having frequent transitions (a minimum of one transition per bit interval) in the signal.
Built-in Error Detection: It is desirable to have a built-in error-detecting capability in the generated
code to detect some of or all the errors that occurred during transmission. Some encoding schemes
that we will discuss have this capability to some extent. Immunity to Noise and Interference Another
desirable code characteristic is a code I that is immune to noise and other interferences. Some
encoding schemes that we will discuss have this capability.
Complexity: A complex scheme is more costly to implement than a simple one. For example, a
scheme that uses four signal levels is more difficult to interpret than one that uses only two levels.
Line Coding Schemes
Line coding
Unipolar
NRZ
Polar
NRZ, RZ,
BiPolar
Multilevel
AMI, Pseudoternary
Biphase(Manchester,
Differential Manchester)
Multitransition
2B/IQ, 8B/6T,
and 4U-PAM5
MLT-3
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Unipolar Scheme
In a unipolar scheme, two voltage levels are used and all the signal levels are on one side of the time
axis, either above or below. NRZ (Non-Return-to-Zero) : In NRZ scheme positive voltage defines
bit 1 and the zero voltage defines bit 0. It is called NRZ because the signal does not return to zero at
the middle of the bit.
In this encoding approach, the bit rate same as data rate. DC component present in the encoded
signal and there is loss of synchronization for long sequences of 0’s and 1’s. The normalized power
(power needed to send 1 bit per unit line resistance) is high compared to other encoding techniques.
For this reasons, this scheme is normally not used in data communications today.
Polar: Polar encoding technique uses two voltage levels – one positive and the other one negative.
NRZ- L
Two different voltages for 0 and 1 bits --- 0= High voltage, 1= Low Voltage
voltage is constant during bit interval no transition i.e. no return to zero voltage
The voltage level is constant during a bit interval; there is no transition (no return to a zero voltage
level). Can have absence of voltage used to represent binary 0, with a constant positive voltage used
to represent binary 1. More commonly a negative voltage represents one binary value and a positive
voltage represents the other.
NRZ –I
0 = No Transition at the beginning of the interval.
1 = Transition at the beginning of the interval.
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NRZI is an example of differential encoding. In differential encoding, the information to be
transmitted is represented in terms of the changes between successive signal elements rather than the
signal elements themselves. The encoding of the current bit is determined as follows: if the current
bit is a binary 0, then the current bit is encoded with the same signal as the preceding bit; if the
current bit is a binary 1, then the current bit is encoded with a different signal than the preceding bit.
One benefit of differential encoding is that it may be more reliable to detect a transition in the
presence of noise than to compare a value to a threshold. Another benefit is that with a complex
transmission layout, it is easy to lose the sense of the polarity of the signal.
• A transition from one voltage level to the
other represents a 1.
Advantages of NRZ
•Detecting a transition in presence of noise is more reliable than to compare a value to a
threshold.
•NRZ codes are easy to engineer and it makes efficient use of bandwidth.
Disadvantages

If there is a long sequence of 0s or 1s in NRZ-L, the average signal power becomes skewed.
The receiver might have difficulty discerning the bit value. In NRZ-I this problem occurs only
for a long sequence of 0s.

The synchronization problem (sender and receiver clocks are not synchronized) also exists in
both schemes.

If twisted-pair cable is the medium, and NRZ-L is the encoding scheme, then a change in
the polarity of the wire results in all 0s interpreted as 1 s and all 1 s interpreted as 0s. NRZ-I
does not have this problem. Both schemes have an average signal rate of N/2 baud.
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
NRZ-L and NRZ-I both have a DC component problem.
RZ – Returned to Zero
This technique uses three values: positive, negative, and zero.
0 = Transition from Low to Zero in the middle of the bit interval.
1 = Transition from High to Zero in the middle of the bit interval.
In RZ, the signal changes not between bits but during the bit. The signal goes to 0 in the middle of
each bit. It remains there until the beginning of the next bit.
Advantages
 No dc component
 Good synchronization
Dis advantages
 Bit rate is double than that of data rate
 Increase in bandwidth
 Complex
Biphase
To overcome the limitations of NRZ encoding, biphase encoding techniques can be adopted.
Manchester and differential Manchester Coding are the two common Biphase techniques
Manchester
0= Transition from high to low in the middle of the interval
1= transition from low to high in the middle of the interval
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Differential Manchester
Always a transition at the middle of the interval
0= Transition at the beginning of the interval
1= No transition at the beginning of the interval
Advantages of Bipolar

Two voltage levels

No DC component

Good synchronization (In Manchester and differential Manchester encoding, the transition
at the middle of the bit is used for synchronization).
 Error Detection (Absence of expected transition can be used to detect errors).
Disadvantages
Higher Bandwidth (High signal rate. The signal rate for Manchester and differential
Manchester is double that for NRZ).
Bipolar AMI
Uses three voltage levels
0 = Zero voltage
1 = Alternate high and low voltages
Advantages
 No DC component
 Lesser bandwidth
Dis advantage
 Loss of synchronization if there is a long sequence of 0s
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Pseudo ternary
Uses three voltage levels
0 = Alternate high and low voltages
1 = Zero voltage
Block Coding
Block coding is normally referred to as mB/nB coding; it replaces each m bit group with an n bit
group.
Redundancy ensure synchronization and to provide some kind of inherent error detecting. Block
coding can give us this redundancy and improve the performance of line coding. In general, block
coding changes a block of m bits into a block of n bits, where n is larger than m. Block coding is
referred to as an mB/nB encoding technique.
Block coding normally involves three steps: division, substitution, and combination.
1. In the division step, a sequence of bits is divided into groups of m bits.
2. The heart of block coding is the substitution step. In this step, we substitute an m-bit group
for an n-bit group.
3. Finally, in the combination step the n-bit groups are combined together to form a stream. The
new stream has more bits than the original bits.
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Example
The four binary/five binary (4B/5B) coding scheme was designed to be used in combination with
NRZ-I. The block-coded stream does not have more than three consecutive 0s. At the receiver, the
NRZ-I encoded digital signal is first decoded into a stream of bits and then decoded to remove the
redundancy.
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.
4-bit Data 5-bit code 4-bit Data 5-bit code
0000
11110
1000
10010
0001
01001
1001
10011
0010
10100
1010
10110
0011
10101
1011
10111
0100
01010
1100
11010
0101
01011
1101
11011
0110
01110
1110
11100
0111
01111
1111
11101
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ANALOG-TO-DIGITAL CONVERSION
Pulse Code Modulation (PCM)
The most common technique to change an analog signal to digital data (digitization) is called pulse
code modulation (PCM). A PCM encoder has three processes,
 Sampling (PAM)
The process of measuring the amplitude of a continuous-time signal at
discrete instants. It converts a continuous-time signal to a discrete-time signal.
 Quantizing Representing the sampled values of the amplitude by a finite set of levels. It
converts a continuous-amplitude sample to a discrete-amplitude sample.
 Encoding
Designating each quantized level by a (binary) code.
Sampling and quantizing operations transform an analogue signal to a digital signal.
The simplest technique for transforming analog data into digital signals is pulse code modulation
(PCM), which involves sampling the analog data periodically and quantizing the samples. Pulse
code modulation (PCM) is based on the sampling theorem. These analog samples, called pulse
amplitude modulation (PAM) samples. To convert to digital, each of these analog samples must be
quantized and assigned a binary code.
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Sampling
The first step in PCM is sampling. The analog signal is sampled every Ts sec, where Ts is the
sample interval or period. The inverse of the sampling interval is called the sampling rate or
sampling frequency (fs). There are three sampling methods-ideal, natural, and flat-top.
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).
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sampling theorem:
If a signal is sampled at regular intervals at a rate higher than twice the highest signal frequency, the
samples contain all information in original signal.
eg. 4000Hz voice data, requires 8000 sample per sec
Example
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 )'/s = 2f (Nyquist rate), and f s =f (one-half the Nyquist rate).
Figure shows the sampling and the subsequent recovery of the signal.
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2. Quantization
The result of sampling is a series of pulses with amplitude values between the maximum and
minimum amplitudes of the signal. These values cannot be used in the encoding process. To convert
PAM signal to digital signal (that is for transmission), each sample has to be ‘rounded up’
to the nearest of L possible quantization levels. This mapping process is called quantization.
The following are the steps in quantization:
1. Assume that the original analog signal has instantaneous amplitudes between Vmin and Vmax
2. Divide the range into L zones, each of height  (delta).
 = Vmax - Vmin
L
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.
3. Assign quantized values of 0 to L – 1 (0, 1, 2,3 ...L-1) to the midpoint of each zone.
4. Approximate the value of the sample amplitude to the quantized values.
Eg :
Assume we have a signal with maximum and minimum amplitude +20 V and -20V respectively.
We decide to have eight levels L = 8 .
So  = 20 – (-20) =5
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PAM Values :
-6.1 7.5
16.2 19.7 11
Quantized values :
-7.5 7.5
17.5 17.5 12.5 -7.5 -12.5 -7.5 -7.5
Quantization code :
Encoded Words :
2
5
010 101
7
7
6
111 111 110
-5.5 -11.3 -9.4 -6.0
2
1
2
2
010 001 010 010
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Quantization Error : One important issue is the error created in the quantization process.
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. The value of the error for any sample is less than /2. In other words, we have /2 < error </2.
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
SNRdB =6.02nb + 1.76 dB
Uniform Versus 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 non uniform 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. 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 non
uniform quantization effectively reduces the SNRdB of quantization.
Encoding
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 n-bit code word. If the number of quantization
levels is L, the number of bits n = log 2 L.
In the above example L is 8 therefore n is 3
The bit rate can be found from the formula
Bit rate = sampling rate x number of bits per sample
= fs x n