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					                            CHAPTER – 5


Model of a communication system:

      The overall purpose of the communication system is to transfer
information from one point to in space and time, called the source to
another point, the user destination. As a rule, the message produced by a
source is not electrical.    Hence an input transducer is required for
converting the message to a time varying electrical quantity called a
message signal. At the destination point another transducer converts the
electrical waveform to the appropriate message.

      The information source and the destination point are usually
separated in space. The channel provides the electrical connection
between the information source and the user. The channel can have many
deferent forms such as a microwave radio link over free space a pair of
wires, or an optical fiber. Regardless of its type the channel degrades the
transmitted single in a number of ways. The degradation is a result of
signal distortion due to imperfect response of the channel and due to
undesirable electrical signals (noise) and interference. Noise and signal
distortion are two basic problems of electrical communication.          The
transmitter and the receiver in a communication system are carefully
designed to avoid signal distortion and minimize the effects of noise at the
receiver so that a faithful reproduction of the message emitted by the
source is possible.
      The transmitter couples the input message signal to the channel.
While it may sometimes be possible to couple the input transducer directly
to the channel, it is often necessary to process and modify the input signal
for efficient transmission over the channel. Signal processing operations
performed   by   the   transmitter   include   amplification,   filtering,   and
modulation. The most important of these operations is modulation a
process designed to match the properties of the transmitted signal to the
channel through the use of a carrier wave.

      Modulation is the systematic variation of some attribute of a carrier
waveform such as the amplitude, phase, or frequency in accordance with a
function of the message signal. Despite the multitude of modulation
techniques, it is possible to identify two basic types of modulation: the
continuous carrier wave (CW) modulation and the pulse nodulation. In
continuous wave (CW) carrier modulation the carrier waveform is
continuous (usually a sinusoidal waveform), and a parameter of the
waveform is changed in proportion to the message signal. In pulse
modulation the carrier waveform is a pulse waveform (often a rectangular
pulse waveform), and a parameter of the pulse waveform is changed in
proportion to the message signal. In both cases the carrier attribute can be
changed in continuous or discrete fashion. Discrete pulse (digital)
modulation is a discrete process and is best suited for messages that are
discrete in nature such as the output of a teletypewriter. However, with the
aid of sampling and quantization, continuously varying (analog) message
signal can be transmitted using digital modulation techniques.

      Modulation is used in communication systems for matching signal
characteristics to channel characteristics, for reducing noise and
interference, for simultaneously transmitting several signals over a single
channel, and for overcoming some equipment limitations. A considerable
portion of this article is devoted to the study of how modulation schemes
are designed to achieve the above tasks. The success of a communication
system depends to a large extent on the modulation.

The main function of the receiver is extract the input message signal from
the degraded version of the transmitted signal coming from the channel.
The receiver performs this function through the process of demodulation,
the reverse of the transmitter’s modulation process. Because of the
presence of noise and other signal degradations, the receiver cannot
recover the message signal perfectly. Ways of approaching ideal recovery
will be discussed later. In addition to demodulation, the receiver usually
provides amplification and filtering.

      Based on the type of modulation scheme used and the nature of the
output of the information source, we can divide communication systems
into three categories:

      1.analog communication systems designed to transmit analog
information using analog modulation methods
      2. digital communication systems designed for transmitting digital
information using digital modulation schemes and
      3. hybrid systems that use digital modulation schemes for
transmitting sampled and quantized values of an analog message signal.

      Other ways of categorizing communication systems include the
classification based on the frequency of the carrier and the nature or the
communication channel
      With this brief description of a general model of a communication
system, we will now take a detailed look at various components that make
up a typical communication system using the digital communication system
as an example. We will enumerate the important parameter of each
functional block in a digital communication system and point out some of
the limitations of the capabilities of various blocks.


      The overall purpose of the system is to transmit the messages (or
sequences of symbols) coming out of a source to a destination point at as
high a rate and accuracy as possible. The source and the destination point
are physically separated in space and a communication channel of some
sort connects the source to the destination point. The channel accepts
electrical/electromagnetic signals, and the output of the channel is usually
a smeared or distorted version of the input due to the non-ideal nature of
the communication channel. In addition to the smearing, the information-
bearing signal is also corrupted by unpredictable electrical signals (noise)
from both man-made and natural causes. The smearing and noise
introduce errors in the information being transmitted and limits the rate at
which information can be communicated from the source to the
destination. The probability of incorrectly decoding a message symbol at
the receiver is often used as a measure of performance of digital
communication system. The main function of the coder, the modulator, the
demodulator, and the decoder is to combat the degrading effects of the
channel on the signal and maximized the information rate and accuracy.
Information source

      Information sources can be classified into two categories based on
the nature of their outputs: Analog information sources, and discrete
information sources. Analog information sources, such as a microphone
actuated by speech, or a TV camera scanning a scene, emit one or more
continuous amplitude signals (or functions of time). The output of discrete
information sources such as a teletype or the numerical output of a
computer consists of a sequence of discrete symbols or letters. An analog
information source can be transformed onto a discrete information source
through the process of sampling and quantizing. Discrete information
sources ate characterized by the following parameters:
      1. Source alphabet (symbols or letters)
      2. Symbol rate
      3. Source alphabet probabilities
      4. Probabilistic dependence of symbols in a sequence
From these parameters, we can construct a probabilistic model of the
information source and define the source entropy (H) and source
information   rate   (R)   in   bits   per   symbol   and   bits   per   second,
respectively.(the term bid is used to denote a binary digit.)

      To develop a feel for what these quantities represent, let us consider
a discrete information source-a teletype having 26 letters of the English
alphabet plus six special characters. The source alphabet for this example
consists of 32 symbols. The symbol rate refers to the rate at which the
teletype produces characters: for purposes of discussion, let us assume
that the teletype operates at a speed of 10 characters or 10 symbols/sec. If
the teletype is producing messages consisting of symbol sequences in the
English language, then we know that some letters will appear more often
than others. We also know that the occurrence of a particular letter in a
sequence is somewhat dependent on the letters preceding it. For example,
the letter E will occur more often than letter Q and the occurrence of Q
implies that the next letter in the sequence will most probably be the letter
U, and so forth. These structural properties of symbol sequences can be
characterized by probabilities of occurrence of individual symbols by the
conditional probabilities of occurrence of symbols.

      An important parameter of a discrete source is its entropy. The
entropy of a source, denoted by H, refers to the average information
content per symbol in a long message and is given units of bits for symbol
where bit is used as an abbreviation for a binary digit. In our example, if we
assume that all symbols occur with equal probabilities in a statistically
independent sequence, then the source entropy is five bits per symbols.
However, the probabilistic dependence of symbols in a sequence, and the
unequal probabilities of occurrence of symbols considerably reduce the
average information content of the symbols. naturally we can justify the
previous statement by convincing ourselves that in a symbol sequence
QUE, the letter U carries little or no information because the occurrence of
Q implies that the next letter in the sequence has to be a U.

      The source information rate is defined as the product of the source
entropy and the symbol rate and has the units of bits per second. The
information rate, denoted by R, represents the minimum number of bits per
second that will be needed, on the average, to represent the information
coming out of the discrete source. Alternately, R represents the Minimum
average data rate needed to convey the information from the source to the
Source Encoder/Decoder

      The input to the source encoder (also referred to as the source
coder) is a string of symbols occurring at a rate of rs symbols/sec. The
source coder converts the symbol sequence into a binary sequence of 0’s
and 1’s by assigning code words to the symbols in input sequence. The
simplest way in which a source coder can perform this operation is to
assign a fixed-length binary code word to each symbol in the input
sequence. For the teletype example we have been discussing, this can be
done by assigning 5-bit code world 00000 through 11111 for the 32
symbols in the source alphabet and replacing each symbol in the input
sequence by its pre-assigned code word.          With a symbol rate of 10
symbols/sec, the source coder output data rate will be 50 bits/sec.

      Fixed-length coding of individual symbols in a source output is
efficient only if the symbols occur with equal probabilities in a statistically
independent sequence. In most practical situation symbols in a sequence
are statistically dependent, and they occur with unequal probabilities. In
these situations the source coder takes a string of two or more symbols as
a block and assigns variable-length code words to these block. The
optimum source coder is designed to produce an output data rate
approaching R, the source information rate. Due to practical constraints,
the actual output rate of source encoders will be greater than the source
information rate R. the important parameters of a source coder are black
size, code word lengths, average data rate, and the efficiency of the coder
(i.e., actual output data rate compared to the minimum achievable rate R).

      At the receiver the source decoder converts the binary output of the
channel decoder into a symbol sequence. The decoder for a system using
fixed-length code words is quite simple, but the decoder for a system using
variable-length code words will be very complex. Decoders for such
systems must be able to cope with a number of problems such as growing
memory requirement and loss of synchronization due to bit errors.

Communication Channel

      The Communication channel provides the electrical connection
between the source and the destination. The channel may be a pair of
wires or a telephone link or free space over which the information bearing
signal is radiated. Due to physical limitations, communication channels
have only finite bandwidth (B HZ), and the information bearing signal often
suffers amplitude and phase distortion as it travels over the channel. In
addition to the distortion, the signal power also decreases due to the
attenuation of the channel. Furthermore, the signal is corrupted by
unwanted, unpredictable electrical signals referred to as noise. While some
of the degrading effects of the of the channel can be removed or
compensated for, the effects of noise cannot be completely removed. From
this point of view, the primary objective of a communication system design
should be to suppress the bad effects of the noise as much as possible.

      One of the ways in which the effects of noise can be minimized is to
increase the signal power. However, signal power cannot be increased
beyond certain levels because of nonlinear effects that become dominant
as the signal amplitude is increased. For this reason the signal-to-noise
power ratio (S/N ), which can be maintained at the output of a
communication channel, is an important parameter of the system. Other
important parameters of the channel are the usable bandwidth (B),
amplitude an phase response, and the statistical properties of the noise.
       If the parameters of a communication channel are known, then we
can compute the channel capacity C, which represents the maximum rate
at which nearly errorless data transmission is theoretically possible.   For
certain types of communication channels it has been shown that c is equal
to B log2 (1+S/N) bits/sec. The channel capacity C has to be greater than
the average information rate R of the source for errorless transmission.
The capacity c represents a theoretical limit, and the practical usable data
rate will be much smaller than C.    as an example, for a typical telephone
link with a usable bandwidth of 3KHz and S/N = 103, the channel capacity
is approximately 30,000 bits/sec. At the present time, the actual data rate
on such channels ranges from 150 to 9600 bits/sec.


      The modulator accepts a bit stream as its input and converts it to an
electrical waveform suitable for transmission over the communication
channel.   Modulation is one of the most powerful tools in the hands of a
communication systems designer.      It can be effectively used to minimize
the effects of channel noise, to match the frequency spectrum of the
transmitted signal with channel characteristics, to provide the capability to
multiplex many signals, and to overcome some equipment limitations.

      The important parameters of the modulator are the types of
waveforms used, the duration of the waveforms, the power level, and the
bandwidth used.    The modulator accomplishes the task of minimizing the
effects of channel noise by the use of large signal power and bandwidth,
and by the use of waveforms that last for longer durations. While the use
of increasingly large amounts of signal power and bandwidth to combat the
effects of noise is an obvious method, these parameters cannot be
increased indefinitely because of equipment and channel limitations. The
use of waveforms of longer time duration to minimize the effects of channel
noise is based on the well-known statistical law of large numbers.      The
law of large numbers states that while the outcome of a single random
experiment may fluctuate wildly, the overall result of many repetitions of a
random experiment can be predicted accurately. In data communications,
this principle can be used to advantage by making the duration of signaling
waveforms long. By averaging over longer durations of time, the effects of
noise can be minimized.

      To illustrate the above principle, assume that the input to the
modulator consists of 0’s and 1’s occurring at a rate of 1 bit/sec. The
modulator can assign waveforms once every second. Notice that the
information contained in the input bit is now contained in the frequency of
the output waveform. To employ waveforms of longer duration, the
modulator can assign waveforms once every four seconds. The number of
distinct waveforms the modulator has to generate (hence the number of
waveforms the demodulator has to detect) increases exponentially as the
duration of the waveforms increases. This leads to an increase in
equipment complexity and hence the duration cannot be increased
indefinitely. The number of waveforms used in commercial digital
modulators available at the present time ranges from 2 to 16.


      Modulation   is   a   reversible   process,   and   the   demodulator
accomplishes the extraction of the message from the information bearing
waveform produced by the modulator. For a given type of modulation, the
most important parameter of the demodulator is the method of
demodulation. There are a variety of techniques available for demodulating
a given modulated waveform: the actual procedure used determines the
equipment complexity needed and the accuracy of demodulation. Given
the type and duration of waveforms used by the modulator, the power level
at the modulator, he physical and noise characteristics of the channel, and
the type of demodulation, we can derive unique relationship between data
rate, power bandwidth requirements, and the probability of incorrectly
decoding a message bit. A considerable portion of this text is devoted to
the derivation of these important relationships and their use in system

Channel Encoder/Decoder

      Digital channel coding is a practical method of realizing high
transmission reliability and efficiency that otherwise may be achieved only
by the use of signals of longer duration in the modulation/demodulation
process. With digital coding, a relatively a small set of analog signals, often
two, is selected for transmission over the channel and the demodulator has
the conceptually simple task of distinguishing between two different
waveforms of known shapes. The channel coding operation that consists
of systematically adding extra bits to the output of the source coder
accomplishes error control. While these extra bits themselves convey no
information, they make it possible for the receiver to detect and/or correct
some of the errors in the information bearing bits.

      There are two methods of performing the channel coding operation.
In the first method, called the block coding method, the encoder takes a
block of k information bits from the source encoder and adds r error control
bits. The number of error control bits added will depend on the value of k
and the error control capabilities desired. In the second method, called the
convolutional coding method, the information bearing message stream is
encoded in a continuous fashion by continuously interleaving information
bits and error control bits. Both methods require storage and processing of
binary data at the encoder and decoder. While this requirement was a
limiting factor in the early days of data communication, it is no longer such
a problem because of the availability of solid-state memory and
microprocessor devices at reasonable prices.

      The important parameters of a channel encoder are the method of
coding. Rate or efficiency of the coder (as measured by the ratio of data
rate at input to the data rate at the output), error controls capabilities, and
complexity of the encoder.

      The channel decoder recovers the information bearing bits from the
coded binary stream. The channel decoder also performs error detection
and possible correction. The decoder operates either in a block mode or in
a continuous sequential mode depending on the type of coding used in the
system. The complexity of the decoder and the time delay involved in the
decoder are important design parameter.

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