EE 421: Communications I
Dr. Mohammed Hawa
Introduction to Digital Baseband Communication Systems
For more information: read Chapters 1 and 7 in your textbook or visit http://wikipedia.org/.
Remember that communication systems in general can be classified into four
categories: Analog Baseband Systems, Analog Carrier Systems (where we use analog
modulation), Digital Baseband Systems and Digital Carrier Systems (where we use
digital modulation).
Digital baseband and digital carrier transmission systems have many advantages
over their analog counterparts. Some of these advantages are:
1. Digital transmission systems are more immune to noise (due to the availability of
regenerative repeaters, which can be used instead of analog amplifiers at
intermediate points throughout the transmission channel).
2. Digital transmission systems allow us to use multiplexing at both the baseband
and carrier levels (e.g., TDMA and CDMA), which means we can easily carry
multiple conversations on a single physical medium (channel).
3. The possibility of using channel coding techniques (i.e., error correcting codes) in
digital communications improves the signal-to-noise ratio (SNR) at the receiver.
4. The ability to use spread spectrum techniques in digital systems help overcome
jamming and interference and allows us to hide the transmitted signal within
noise if necessary.
5. Using computers to perform signal processing (DSP) on digital signals eliminates
the need to build expensive and bulky discrete-component devices.
Actually, due to these important advantages many communication systems are
transitioning these days from analog to digital communications. Within the next
decade most of communication will become digital, with analog communication
playing a minor role.
This article provides a very quick overview of some of the main concepts that are
relevant to digital baseband transmission. You will study more about this topic in the
EE422 “Communications II” course. The main concepts to be emphasized here will
be the analog-to-digital conversion process and the line coding technique.
Analog-to-Digital (A/D) Conversion:
Signals that result from physical phenomena (such as voice or video) are almost
always analog baseband signals. Such analog baseband signals can be converted into
digital baseband signals using the following steps:
1. Sampling (in which the signal becomes a sampled analog signal, also called a
discrete analog signal).
2. Quantization (the signal becomes a quantized discrete signal, but not a digital
signal yet).
3. Mapping (the signal becomes a stream of 1’s and 0’s).
4. Encoding and Pulse Shaping (after which the signal becomes a digital baseband
signal).
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These four steps are shown in the Figure below and are explained in the following
subsections.
Digital
Baseband
Analog
Digital
Signal
Digital
Baseband
A/D
Carrier
Modulation
Signal
Signal
Sampling
Quantization
Mapping
Source
Encoding
Encoding &
Pulse Shaping
Channel
Encoding
Line
Encoding
I. Sampling:
Sampling is the process in which only a relatively-small set of values, called discrete
samples {mn}, are taken to represent the signal m(t) instead of the (time-continuous)
infinite set of values included in the analog signal (see the following figure).
In uniform sampling, the time interval between successive samples is set to a constant
value equal to T, called the sampling time. In this case, the sampling frequency is
fs = 1/T.
Nyquist–Shannon sampling theorem states that for the samples {mn} to truly represent
the original signal m(t), we need the sampling frequency fs to be at least twice as high
as the bandwidth B of the band-limited analog signal m(t) (i.e., fs ≥ 2B). Such a
condition will prevent aliasing. Aliasing should be avoided at all costs since it means
that the signal m(t) cannot be recovered from the discrete samples {mn} by simple
low-pass filtering at the receiver.
As specific examples, telephone conversations are sampled at 8 kHz (twice the
4 kHz bandwidth of the human voice signal), while compact disc (CD) audio is
sampled at 44.1 kHz (twice the 22.05 kHz bandwidth of music signals1).
Some music instruments generate signals with bandwidths exceeding 22.05 kHz but a human ear
cannot hear sounds above the 20 kHz mark.
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2
II. Quaantization::
Quantiization is the
t processs in which each samp
ple value is
i approxim
mated or “ro
ounded
off” to a relativeely-small set of discrrete quantizzation levells. For exaample, in uniform
u
quantizzation if th
he amplitu
ude of thee signal m((t) lies in the
t range (-mp, mp), we can
partitio
on this con
ntinuous raange into L discrete intervals,
i
e
each
of len
ngth Δv = 2 mp /L,
and thee value of each samp
ple is then approxim
mated to on
nly one of tthese L lev
vels (see
Figure below).
ny, for exaample, thee number of
o quantizaation levells is choseen to be
In voicce telephon
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L = 2 = 256, while for compact disc (CD)
(
audio
o, the numb
ber of quaantization levels
l
is
L = 2166 = 65,536 possible
p
values per sample.
s
Of course, a bigger vaalue of L means
m
a
smallerr interval Δv,
Δ and heence a smaaller round
d off error caused by
y the quanttization
processs (called qu
uantization error).
The nu
umber of quantizatio
q
on levels L is an im
mportant paarameter in digital systems
s
becausse it decidees (see nex
xt step) how
w many biits will be used to reepresent th
he value
of each
h sample. For
F examp
ple, if L = 256,
2
which
h means thaat the valu
ue of each sample
can be one of 256 possibiliities, then each samp
ple must be
b mapped
d (encoded
d) into 8
bits. This is beccause 8 bin
nary bits can be in
n 28 = 2566 possible states (00
0000000,
000000001, 000000010, 00000011, . . ., 11111111).. For L = 65,536, wee need 16 bits to
encodee each sam
mple value.
III. Maapping:
Digitall systems use
u mostly
y binary coding, in which eacch of the q
quantized sample
values (e.g., 6V, 10V,
1
etc) iss mapped (encoded) to a correesponding binary cod
de (e.g.,
0110, 1010, etc). The
T result is
i a stream of 1’s and 0’s.
Notice that each sample is representted by log2 (L) bits, and
a
hence the bit tim
me T0 is
given by
b T0 = T / log2 (L), where
w
T is the samplle period.
The tottal numberr of bits geenerated in
n one secon
nd is called
d the data b
bit rate f0 = 1 / T0
measurred in bits/
/s (or bps) is given by:
b
f0 [bps] = fs [samples/s] × log
g2 (L) [bits/
/sample]
d Pulse Sh
haping:
IV. Enccoding and
Encodiing is the final step
p in whatt we call analog-to-digital (A
A/D) conv
version.
Sometiimes, enco
oding is co
onsidered as
a a separa
ate stage that
t
follow
ws the A/D
D stage,
which takes a bitt stream off 1’s and 0’s
0 and con
nverts it in
nto voltagees approprriate for
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transmission on a physical channel. Encoding schemes are usually divide into:
Source coding, Channel coding and Line coding (see Figure in page 2).
A. Source coding: Source coding (sometimes called entropy encoding) refers to the
process of remapping binary codes (named codewords) to new ones so as to match
code lengths with the probabilities of their occurrence in the bit stream. For example,
a 4-bit sequence “0110” occurring frequently can be mapped to the shorter 2-bit “01”
sequence, while another 4-bit sequence “1011” occurring less frequently can be
mapped to the longer 7-bit sequence “0011011”. This makes sure that shorter
sequences occur more often in the bit stream.
Typically, source encoders are used to compress data by replacing long symbols that
occur frequently by shorter codes, and those that occur less frequently by longer
codes. In information theory, Shannon's noiseless coding theorem places an upper
and a lower bound on the expected compression ratio. Examples of source codes
currently in use are: Shannon codes, Huffman codes, run-length coding, arithmetic
coding, Lempel-Ziv coding, MPEG video coding, etc.
B. Channel coding: a channel code is a broadly used term mostly referring to error
correcting codes. Such codes are used to protect data sent over the channel from
corruption even in the presence of noise. In other words, channel codes can improve
the signal-to-noise ratio (SNR) of the received signal.
The theory behind designing and analyzing channel codes is called Shannon’s noisy
channel coding theorem. It puts an upper limit on the amount of information you
can send in a noisy channel as shown in the following equation:
log 1
where C is the upper bound on the capacity of the channel (bit/s), B is the bandwidth
of the channel (Hz) and SNR is the Signal-to-Noise ratio (unitless). Examples of
channel codes currently in-use include: Hamming codes, Reed-Solomon codes,
convolutional codes (usually decoded by an iterative Viterbi decoder), Turbo codes,
etc.
C. Line coding: In telecommunications, Line coding refers to the process of
representing the bit stream (1’s and 0’s) generated by a source in the form of
variations of voltage or current optimally tuned for the specific properties of the
physical channel being used.
The selection of a proper line code can help in so many ways: One possibility is to
help in reliable clock recovery at the receiver. A clock signal is recovered by
observing transitions in the received bit sequence, and if enough transitions exist, a
good recovery of the clock is guaranteed, and the signal is said to be self-clocking.
Another advantage is to get rid of DC shifts. The DC component in a line code is
called the bias or the DC coefficient. Unfortunately, most long-distance
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communication channels cannot transport a DC component2. This is why most line
codes try to eliminate the DC component – such codes are called DC balanced, zeroDC, zero-bias, or DC equalized.
Some common types of line encoding in common-use nowadays are unipolar, polar,
bipolar, Manchester, etc encoding. These codes are explained here:
1. Unipolar (Unipolar NRZ and Unipolar RZ):
Unipolar is the simplest line coding scheme possible. It is almost obsolete today, but
it has the advantage of being compatible with TTL logic. It uses a positive
rectangular pulse p(t) to represent binary 1, and the absence of a pulse (i.e., zero
voltage) to represent a binary 0.
Two possibilities for the pulse p(t) exist3: Non-Return-to-Zero (NRZ) rectangular
pulse and Return-to-Zero (RZ) rectangular pulse. The difference between Unipolar
NRZ and Unipolar RZ codes is that the rectangular pulse in NRZ stays at a positive
value (e.g., +5V) for the full duration of the logic 1 bit, while the pule in RZ drops
from +5V to 0V in the middle of the bit time. The figure below4 shows the difference
between Unipolar NRZ and Unipolar RZ for the example bit stream 1110110001001.
Clock
1
Data
1
1
0
1
1
0
0
0
1
0
0
1
Code
0
T0
Bit time
T
Sampling time (assuming 8 bits per sample)
Unipolar NRZ Code
Unipolar RZ Code
DC-values create excessive heat generation in the channel, they cause baseline drift and also do not
fit systems that carry an additional small direct current to power intermediate line amplifiers (an
example is telephone networks).
3 Actually there are so many possibilities for the pulse shape p(t), not just a rectangular NRZ or
rectangular RZ pulses. Changing p(t) waveform is called Pulse Shaping and is considered a major
part of line coding. The pulse shape selected affects the characteristics of the line code. Here we will
limit ourselves to rectangular pulses.
4 To investigate the same line code for other bit streams you can use the Code Analyzer software
available at http://www.grega.phpnet.us/analizator/.
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5
A drawback of unipolar (RZ and NRZ) is that its average value is not zero, which
means it creates a significant DC-component at the receiver (see the impulse at zero
frequency in the corresponding power spectral density (PSD) of this line code shown
in the diagram below). As we explained earlier, a DC-value is not desired in longdistance communication systems. Another disadvantage of such unipolar (RZ and
NRZ) signaling is that it does not include clock information especially when the bit
stream consists of a long sequence of 0’s.
The disadvantage of unipolar RZ compared to unipolar NRZ is that each rectangular
pulse in RZ is only half the length of NRZ pulse. This means that unipolar RZ
requires twice the bandwidth of the NRZ code. This can be seen from the PSD of
both signals shown below.
2. Polar (Polar NRZ and Polar RZ):
In Polar NRZ line coding binary 1’s are represented by a pulse p(t) (e.g., +5V) and
binary 0’s are represented by the negative of this pulse -p(t) (e.g., -5V). Polar signals
(NRZ and RZ) are shown in the diagram below.
Polar NRZ Code
Polar RZ Code
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Using the assumption that in a regular bit stream a logic 0 is just as likely as a logic 1,
polar signals (whether RZ or NRZ) have the advantage that the resulting DCcomponent is very close to zero.
In addition, the rms value of polar signals is bigger than unipolar signals, which
means that polar signals have more energy than unipolar signals, and hence have
better SNR at the receiver. Actually, polar NRZ signals have even more energy than
polar RZ signals.
The drawback of polar NRZ, however, is that it lacks clock information especially
when a long sequence of 0’s or 1’s is to be transmitted. This problem does not exist in
polar RZ signals, since the signal drops to zero in the middle of each pulse period.
The power spectral densities (PSD) of both polar NRZ and polar RZ are shown
below.
Signals transmitted on a computer motherboard often use Polar NRZ code. Another
useful application of this encoding is in Fiber-based Gigabit Ethernet (1000BASE-SX
and 1000BASE-LX).
Note: Polar NRZ is often just called NRZ. Polar RZ is often just called RZ.
A variant of Polar NRZ is Non-Return-to-Zero-Level (NRZ-L) in which the 1’s and
0’s are represented by -p(t) and p(t), respectively. This is Polar NRZ using negative
logic. As an example, NRZ-L is used in the RS-232 serial port communication.
NRZ-L Code
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3. Non-Return-to-Zero, Inverted (NRZI):
NRZI is a variant of Polar NRZ. In NRZI there are two possible pulses, p(t) and –p(t).
A transition from one pulse to the other happens if the bit being transmitted is a
logic 1, and no transition happens if the bit being transmitted is a logic 0.
NRZI Code5
This is the code used on compact discs (CD), USB, and on fiber-based Fast Ethernet
at 100-Mbit/s (100Base-FX).
NRZI can achieve synchronization between the transmitter and receiver, if we make
sure that there are enough umber of 1’s in the transmitted bit stream.
4. Bipolar encoding (also called Alternate Mark Inversion (AMI)):
Bipolar (or AMI) is a three-level system that uses p(t), -p(t), and grounded pulses
(e.g. +5V, -5V, 0V) to represent logical values. A logic 0 is represented with a
grounded or absent pulse, and a logic 1 by either a positive or negative pulse. The
direction of the pulse is opposite of the pulse sent for the previous logic 1 (mark).
Bipolar (AMI) Code
The alternating code in bipolar encoding prevents the build-up of a DC voltage in
the cable. You can observe the absence of low frequencies (including the DC
component) from the PSD shown below.
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NRZI is always polar not unipolar.
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Line Code
Unipolar NRZ
Unipolar RZ
Polar NRZ
Polar RZ
Bipolar NRZ
Duobinary
Bandwidth
f0
2 f0
f0
2 f0
f0
f0 / 2
AMI coding was used extensively in first-generation digital telephony PCM
networks. AMI suffers the drawback that a long run of 0's produces no transitions in
the data stream, and a loss of synchronization is possible. This was solved in
telephony by adopting other encoding schemes (which are improved versions of
AMI) to ensure regular transitions in the baseband signal even for long runs of 0’s.
The Binary-with-8-Zero-Substitution (B8ZS) is a newer line coding scheme that was
adopted for North America T1 system, while High-Density Bipolar 3-Levels
(HDB3) was the line coding scheme used in the European E1 system.
Note: A very similar encoding scheme to AMI, with the logical positions reversed, is
also used and is often referred to as pseudoternary encoding. This encoding is
essentially identical to AMI, with marks (1’s) being zero voltage and spaces (0’s)
alternating between positive and negative pulses.
Note: Coded Mark Inversion (CMI) is another variation of AMI, where 0 bits are
represented by a transition in the middle of the bit time instead of zero voltage.
5. Multi-Level Transmission 3-Levels (MLT-3):
MLT-3, covered by US Patent 5,280,500, is used mainly in 100BASE-TX Fast Ethernet,
which is the most common type of Ethernet. MLT-3 cycles through the states -p(t), 0,
p(t), 0, -p(t), 0, p(t), 0, ... etc. It moves to the next state to transmit a 1 bit, and stays in
the same state to transmit a 0 bit.
MLT-3 Code
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MLT-3 has many advantages including emitting less Electromagnetic interference,
requiring less bandwidth than unipolar, bipolar and AMI signals operating at the
same data bit rate.
6. Duobinary:
A duobinary signal is a signal in which a 0 bit is represented by a zero-level electric
voltage; a 1 bit is represented by a p(t) if the quantity of 0 bits since the last 1 bit is
even, and by -p(t) if the quantity of 0 bits since the last 1 bit is odd. An illustration of
the duobinary signaling is shown below.
Duobinary Code
For a bit rate of f0, duobinary signaling requires f0/2 bandwidth, which is the
minimum possible (theoretical) bandwidth for any digital baseband signal (called
Nyquist bandwidth). In addition, duobinary signaling permits the detection of some
transmission errors without the addition of error-checking bits. However, duobinary
signals have significant low frequency components as seen by the PSD shown
earlier. The differential version of the duobinary signaling is common in the
20 Gbit/s and 40 Gbit/s uncompensated optical fiber transmission systems.
7. Manchester:
Currently there are two opposing conventions for the representation of Manchester
codes:
The first convention of these was first published by G. E. Thomas in 1949 and is
followed by numerous authors (e.g., Andrew S. Tanenbaum). It specifies that for a 0
bit the signal levels will be Low-High with a low level in the first half of the bit
period, and a high level in the second half (see figure below). For a 1 bit the signal
levels will be High-Low.
The second convention is also followed by numerous authors (e.g., Stallings) as well
as by IEEE 802.4 and IEEE 802.3 (Ethernet 10 Mbps 10Base-T) standards. It states
that a logic 0 is represented by a High-Low signal sequence and a logic 1 is
represented by a Low-High signal sequence.
If a Manchester encoded signal gets inverted somewhere along the communication
path, it transforms from one variant to another. In this article, we will adopt the first
convention (see figure below).
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Manchester Code6
In Manchester code each bit of data is signified by at least one transition. Manchester
encoding is therefore considered to be self-clocking, which means that accurate clock
recovery from a data stream is possible. In addition, the DC component of the
encoded signal is zero.
Although transitions allow the signal to be self-clocking, it carries significant
overhead as there is a need for essentially twice the bandwidth of a simple NRZ or
NRZI encoding (see the PSD below). This is the main disadvantage of this encoding
scheme.
Line Code
Polar NRZ
Polar RZ
Manchester
Bandwidth
f0
2 f0
2 f0
8. Differential Manchester encoding
In Differential Manchester encoding a 1 bit is indicated by making the first half of the
signal equal to the last half of the previous bit’s signal i.e. no transition at the start of
the bit-time. A 0 bit is indicated by making the first half of the signal opposite to the
last half of the previous bit's signal i.e. a zero bit is indicated by a transition at the
beginning of the bit-time.
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Manchester is always polar not unipolar.
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Differential Manchester Code
Because only the presence of a transition is important, differential schemes will work
exactly the same if the signal is inverted (wires swapped).
In the middle of the bit-time there is always a transition, whether from high to low,
or low to high, which provides a clock signal to the receiver.
Differential Manchester is specified in the IEEE 802.5 standard for IBM Token Ring
LANs, and is used for many other applications, including magnetic and optical
storage.
9. M-ary Coding
In binary line coding, the number of bits per second is the same as the number of
symbols per second. We say that for binary signaling:
data bit rate [in units of bit/s] = symbol rate [in units of baud]
Notice that a symbol is defined as a waveform pattern that the line code has for a
certain period of time before switching to another waveform pattern (i.e., another
symbol).
In M-ary signaling, a cluster of bits is grouped to represent one symbol. For example,
in the 4-ary (also called Quaternary) case, two bits are grouped into one symbol. The
two bits can be in one of 4 possible states, which means that the symbol can take M =
4 different values. The following table shows a possible mapping of bit values to
symbol values, and an example of how such line code works for a particular bit
stream is shown next.
Bits
00
01
10
11
Symbol value
-5 V
-10 V
5V
10 V
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4-ary Code
Notice that a symbol time Ts is now twice the bit time T0. This means that there are
half as much symbol transitions as there are bit transitions. We can say that:
symbol rate [in units of baud] = (½) × data bit rate [in units of bit/s]
For a general M-ary coding scheme, we have:
symbol rate [in units of baud] = (1/log2 (M)) × data bit rate [in units of bit/s]
where M is the number of levels (possibilities) for a symbol. Such a drop in transition
rate in the resulting signal will reduce the bandwidth of the signal by a factor of
log2 (M).
Note: You can see various line codes and their corresponding power spectral
densities if you run the Code Analyzer at: http://www.grega.phpnet.us/analizator/
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