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A.SANYSI RAO
                     AMIE; M.Tech; MISTE; MIETE

            Assoc. Professor
Balaji Institute of Engineering & Sciences
            A.S.Rao
Transformation of Information to Signals




                       A.S.Rao
Bandwidth




            A.S.Rao
Bit Rate and Bit Interval




                        A.S.Rao
Corruption Due to Insufficient Bandwidth




                      A.S.Rao
Objective                To send information

                 •Reliability
                 •As fast as possible

Constraints              Rules of the GAME

                 •Limited transmit power
                 •Limited Channel Bandwidth

In our control           We get to DESIGN the

                 •Transmitter
                 •Receiver
                                  as long they follow the rules of the GAME.

Major Tools
                 •Signals & Systems
                 •Probability Theory
                                   A.S.Rao
Analog versus Digital
It is harder to separate noise from an analog signal than it is to
separate noise from a digital signal.




Noise in a digital signal. You can still discern a high voltage from a low
voltage.




                                  A.S.Rao
A.S.Rao
Bandwidth for Telephone Line




                     A.S.Rao
A.S.Rao
A.S.Rao
Parallel Transmission




                        A.S.Rao
Serial Transmission




                      A.S.Rao
Asynchronous Transmission




                     A.S.Rao
Synchronous Transmission




                    A.S.Rao
Ideal pulse shapes.




Non ideal pulse shape.




                         A.S.Rao
A.S.Rao
Core Concepts of
Digital Communications


          A.S.Rao
Elements of a Digital Communication System


  Source of    Source      Channel
                                         Modulator
Information   Encoder      Encoder




                        Binary Stream      Channel




   Use of      Source      Channel
                                        Demodulator
Information   Decoder      Decoder
Modified Diagram of a Digital Communication System

                                                    From other Sources


 Source of     Source                      Channel
                         Encryptor                       MUX           Modulator
Information   Encoder                      Encoder



                                                                        Channel




   Use of      Source                     Channel       DE-
                        Decryptor                                 Demodulator
Information   Decoder                     Decoder       MUX


                                                    To other Sources
                                A.S.Rao
• Can withstand channel noise and distortion much better as long
  as the noise and the distortion are within limits.

• Regenerative repeaters prevent accumulation of noise along the
  path.

• Digital hardware implementation is flexible.

• Digital signals can be coded to yield extremely low error rates,
  high fidelity and well as privacy.

• Digital communication is inherently more efficient than analog in
  realizing the exchange of SNR for bandwidth.

• It is easier and more efficient to multiplex several digital signals.
                                 A.S.Rao
• Digital signal storage is relatively easy and inexpensive.

• Reproduction with digital messages is extremely reliable without
  deterioration.

• The cost of digital hardware continues to halve every two or
  three years, while performance or capacity doubles over the
  same time period.



Disadvantages

•   TDM digital transmission is not compatible with the FDM

•   A Digital system requires large bandwidth.
                                 A.S.Rao
PCM System




             A.S.Rao
A.S.Rao
A.S.Rao
•Quantization process
•Quantization Error
•Mean Square Value of Quantization Noise
•SNR of PCM system
               A.S.Rao
M  S   Q.E  n   S/N   BW 
                 A.S.Rao
A.S.Rao
   Many signals such as speech have a nonuniform distribution.

     –    The amplitude is more likely to be close to zero than to be at higher levels.

   Nonuniform quantizers have unequally spaced levels


                              Output sample
                                              6



                                              4



                                              2




                         -8   -6   -4   -2                  2   4   6      8

                                             -2
                                                                        Input sample


                                             -4



                                             -6   A.S.Rao
A.S.Rao
Companding          in PCM
•Non-uniform quantizers are expensive and difficult to make.
•An alternative is to first pass the speech signal through a non
linearity before quantizing with a uniform quantizer.
•The non linearity causes the signal amplitude to be compressed. So
the input to the quantizer will have a more uniform distribution.
•At the receiver, the signal is expanded by an inverse to the
nonlinearity.
•The process of compressing and expanding is called Companding.




                                A.S.Rao
compression+expansion               companding


                                                                 ˆ
                                                                 x
x(t )                   y (t )                          ˆ
                                                        y (t )                      ˆ
                                                                                    x(t )


                   x                                                            ˆ
                                                                                y
        Compress                 Uniform Qauntize                    Expand
                       Transmitter                     Channel       Receiver




                                             A.S.Rao
A.S.Rao
Telephones in US, Canada and Japan use -law Companding. (=255)

A-Law is used elsewhere to compress digital telephone signals.
                                A.S.Rao
A.S.Rao
A.S.Rao
Digital Formats




                  A.S.Rao
Differential PCM




                   A.S.Rao
•PCM is powerful, but quite complex coders and decoders are
required.

•An increase in resolution also requires a higher number of bits per
sample.

•The Delta Modulation is the most economical form of Digital
Communication System since it requires only one bit per sample
(either low pulse or high pulse) transmitted through the line.

•Delta Modulation uses a single-bit PCM code to achieve digital
transmission of analog signals.

•Normally Sampled at high rate.
                                  A.S.Rao





  When the step is decreased, ‘0’ is transmitted and if it
  is increased, ‘1’ is transmitted.

Delta Modulation: Unique Features
1. No need for Word Framing because of one-bit code word.

2. Simple design for both Transmitter and Receiver.
                             A.S.Rao
DM Transmitter




                 A.S.Rao
DM Receiver




Limitations / Problems of DM system

        •Slope over load error
        •Granular error (or) Hunting

                             A.S.Rao
Slope overload - when the analog input signal changes at a faster
rate than the DAC can maintain. The slope of the analog signal is
greater than the delta modulator can maintain and is called slope
overload.




Granular noise - It can be seen that when the original analog input
signal has a relatively constant amplitude, the reconstructed signal
has variations that were not present in the original signal. This is
called granular noise. Granular noise in delta modulation is
analogous to quantization noise in conventional PCM.



                                 A.S.Rao
A.S.Rao
A.S.Rao
M- ary Signaling

Multiple Signal Levels:
Why use multiple signal levels?
We can represent two levels with a single bit, 0 or 1.
We can represent four levels with two bits: 00, 01, 10, 11.
We can represent eight levels with three bits: 000, 001,
010, 011, 100, 101, 110, 111
Note that the number of levels is always a power of 2.
                          M=2n
                            A.S.Rao
DIGITAL MODULATION




Input Binary
data
                               Output Symbol/waveform



                     A.S.Rao
GOALS OF MODULATION TECHNIQUES

• Low cost and ease of implementation

• Low carrier-to-co channel interference ratio

• Low-Cost/Low-Power Implementation

• High Power Efficiency

• High Bit Rate

• High Spectral Efficiency

                             A.S.Rao
Bit Rate Vs Baud Rate
Bit rate is the number of bits per second. Baud rate is the number of
signal units (symbols) per second. Baud rate is less than or equal to
the bit rate.




                                A.S.Rao
Modulation     Units             Bits/Baud   Baud rate   Bit Rate

ASK, FSK, 2-PSK     Bit                 1           N           N

4-PSK, 4-QAM       Dibit                2           N          2N

8-PSK, 8-QAM       Tribit               3           N          3N

16-QAM            Quadbit               4           N          4N

32-QAM            Pentabit              5           N          5N

64-QAM            Hexabit               6           N          6N

128-QAM           Septabit              7           N          7N

256-QAM           Octabit               8           N          8N
                           A.S.Rao
A.S.Rao
ASK




FSK




      A.S.Rao
PSK




      A.S.Rao
QPSK




       A.S.Rao
8 PSK




        A.S.Rao
The 4-QAM and 8-QAM constellations




                        A.S.Rao
Time domain representation for an 8-QAM signal




                         A.S.Rao
16-QAM constellations




                        A.S.Rao
Detection
            • Coherent Detection

            • Non Coherent Detection


Bandwidth Efficiency
                     Data Transmission Rate , rb
             BW 
                      M inimum Bandwidth, B
                 2
             B
                TS
                     log 2 M
             BW 
                        2

             M    BW 
                               A.S.Rao
Matched Filter



The ultimate task of a receiver is detection, i.e. deciding between
1’s and 0’s. This is done by sampling the received pulse and
making a decision
Matched filtering is a way to distinguish between two pulses
with minimum error




                               A.S.Rao
Im pulse response of the Matched Filter is
        2K
h(t )     x(T  t )
        N0




           A.S.Rao
A.S.Rao
Inter Symbol Interference




                       A.S.Rao
• A sinc pulse has periodic zero crossings. If successive bits
  are positioned correctly, there will be no ISI at sampling
  instants.



                                         Sampling Instants
                                         ISI occurs but,
                                         NO ISI is present at the
                                         sampling instants




                             A.S.Rao
Raised Cosine Filter




                       A.S.Rao
EYE DIAGRAMS
  The eye diagram provides visual information that can be useful
  in the evaluation and troubleshooting of digital transmission
  systems.

  It provides at a glance evaluation of system performance and
  can offer insight into the nature of channel imperfections,




   Top: Undistorted eye diagram of a band limited digital signal
   Bottom: Eye diagram includes amplitude (noise) and phase (timing) errors
                                      A.S.Rao
A.S.Rao
Eye Pattern formation




                        A.S.Rao
Information Theory


• It is a study of Communication Engineering plus
  Maths.

• A Communication Engineer has to Fight with
     • Limited Power
     • Inevitable Background Noise
     • Limited Bandwidth




                            A.S.Rao
P varies as e  KEb
      e

     S i  Eb Rb         Eb  Si / Rb
     Eb   S i            or          Rb   Eb 

Hartley Shannon has shown that
       “If the rate of information from a source does not exceed
the capacity of a given communication channel, then there exists
a coding technique such that the information can be transmitted
over the channel with arbitrary small frequency errors, despite
the presence of noise.”

Information theory deals with the following three basic concepts:
       •The measure of source information
       •The information capacity of a channel
       •Coding                A.S.Rao
Information Sources:
       •Analog Information Source
       •Discrete Information Source

Information Measure
Consider two Messages
A Dog Bites a Man  High probability  Less information
A Man Bites a Dog  Less probability  High Information


       Information α (1/Probability of Occurrence)

The basic principle involved in determining the information
content of a message is that “the information content of a
message increases with its uncertainty”
                              A.S.Rao
Let I(mK) the information content in the Kth message.

  I ( mk )  0                   for PK 1
  I ( mk )  I ( m j )           for PK  Pj                         1
  I ( mk )  0                   for 0  Pk  1

  I (mk and m j )  I (mk m j )  I (mk )  I (m j )                 2

                                          1    
                         I (mk )  log b 
                                         P     
                                                
                                          k    

The quantity I(mk) is called the Self information of message mk.
                                                                 1
The self information convey the message is             I  log
                                                                 P
                                      A.S.Rao
Coding

  Why Coding?

  • to achieve reliable data communication
  • to achieve reliable data storage
  • to reduce the required transmit power
  • to reduce hardware costs of transmitters
  • to improve bandwidth efficiency
  • to increase channel utilisation
  • to increase storage density




                                  A.S.Rao
• Source Coding
         • Channel Coding




Source Coding
          • Shannon Fano Code
          • Huffman Code

Channel Coding
         • Linear Block Codes
                 •Cyclic Codes
         • Convolutional Codes
                            A.S.Rao
Shannon Fano Source code

Algorithm.

Step 1: Arrange all messages in descending order of probability.

Step 2: Divide the Seq. in two groups in such a way that sum of
   probabilities in each group is same.

Step 3: Assign 0 to Upper group and 1 to Lower group.

Step 4: Repeat the Step 2 and 3 for Group 1 and 2 and So on……..




                                A.S.Rao
Messages
               Pi   Coding Procedure          No. Of   Code
  Mi                                           Bits

M1         ½        0                         1        0

M2         1/8/     1   0   0                 3        100

M3         1/8      1   0   1                 3        101

M4         1/16     1   1   0       0         4        1100

M5         1/16     1   1   0       1         4        1101

M6         1/16     1   1   1        0        4        1110

M7         1/32     1   1   1        1    0   5        11110

m8         1/32     1   1   1        1    1   5        11111

                                A.S.Rao
HUFFMAN CODING




                 A.S.Rao
SHANNON HARTLEY CHANNEL CAPACITY THEOREM

                                 S
                  C  B log 2 1  
                                 N


Channel Capacity with Infinite Bandwidth

                                                    C
                  S
    Lt C  1.44                          1.44
                                                S
   B                                         



                                                        B

                               A.S.Rao
A.S.Rao

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Digital communications

  • 1. A.SANYSI RAO AMIE; M.Tech; MISTE; MIETE Assoc. Professor Balaji Institute of Engineering & Sciences A.S.Rao
  • 2. Transformation of Information to Signals A.S.Rao
  • 3. Bandwidth A.S.Rao
  • 4. Bit Rate and Bit Interval A.S.Rao
  • 5. Corruption Due to Insufficient Bandwidth A.S.Rao
  • 6. Objective To send information •Reliability •As fast as possible Constraints Rules of the GAME •Limited transmit power •Limited Channel Bandwidth In our control We get to DESIGN the •Transmitter •Receiver as long they follow the rules of the GAME. Major Tools •Signals & Systems •Probability Theory A.S.Rao
  • 7. Analog versus Digital It is harder to separate noise from an analog signal than it is to separate noise from a digital signal. Noise in a digital signal. You can still discern a high voltage from a low voltage. A.S.Rao
  • 9. Bandwidth for Telephone Line A.S.Rao
  • 16. Ideal pulse shapes. Non ideal pulse shape. A.S.Rao
  • 18. Core Concepts of Digital Communications A.S.Rao
  • 19. Elements of a Digital Communication System Source of Source Channel Modulator Information Encoder Encoder Binary Stream Channel Use of Source Channel Demodulator Information Decoder Decoder
  • 20. Modified Diagram of a Digital Communication System From other Sources Source of Source Channel Encryptor MUX Modulator Information Encoder Encoder Channel Use of Source Channel DE- Decryptor Demodulator Information Decoder Decoder MUX To other Sources A.S.Rao
  • 21. • Can withstand channel noise and distortion much better as long as the noise and the distortion are within limits. • Regenerative repeaters prevent accumulation of noise along the path. • Digital hardware implementation is flexible. • Digital signals can be coded to yield extremely low error rates, high fidelity and well as privacy. • Digital communication is inherently more efficient than analog in realizing the exchange of SNR for bandwidth. • It is easier and more efficient to multiplex several digital signals. A.S.Rao
  • 22. • Digital signal storage is relatively easy and inexpensive. • Reproduction with digital messages is extremely reliable without deterioration. • The cost of digital hardware continues to halve every two or three years, while performance or capacity doubles over the same time period. Disadvantages • TDM digital transmission is not compatible with the FDM • A Digital system requires large bandwidth. A.S.Rao
  • 23. PCM System A.S.Rao
  • 26. •Quantization process •Quantization Error •Mean Square Value of Quantization Noise •SNR of PCM system A.S.Rao
  • 27. M  S   Q.E  n   S/N   BW  A.S.Rao
  • 29. Many signals such as speech have a nonuniform distribution. – The amplitude is more likely to be close to zero than to be at higher levels.  Nonuniform quantizers have unequally spaced levels Output sample 6 4 2 -8 -6 -4 -2 2 4 6 8 -2 Input sample -4 -6 A.S.Rao
  • 31. Companding in PCM •Non-uniform quantizers are expensive and difficult to make. •An alternative is to first pass the speech signal through a non linearity before quantizing with a uniform quantizer. •The non linearity causes the signal amplitude to be compressed. So the input to the quantizer will have a more uniform distribution. •At the receiver, the signal is expanded by an inverse to the nonlinearity. •The process of compressing and expanding is called Companding. A.S.Rao
  • 32. compression+expansion companding ˆ x x(t ) y (t ) ˆ y (t ) ˆ x(t ) x ˆ y Compress Uniform Qauntize Expand Transmitter Channel Receiver A.S.Rao
  • 34. Telephones in US, Canada and Japan use -law Companding. (=255) A-Law is used elsewhere to compress digital telephone signals. A.S.Rao
  • 37. Digital Formats A.S.Rao
  • 38. Differential PCM A.S.Rao
  • 39. •PCM is powerful, but quite complex coders and decoders are required. •An increase in resolution also requires a higher number of bits per sample. •The Delta Modulation is the most economical form of Digital Communication System since it requires only one bit per sample (either low pulse or high pulse) transmitted through the line. •Delta Modulation uses a single-bit PCM code to achieve digital transmission of analog signals. •Normally Sampled at high rate. A.S.Rao
  • 40.  When the step is decreased, ‘0’ is transmitted and if it is increased, ‘1’ is transmitted. Delta Modulation: Unique Features 1. No need for Word Framing because of one-bit code word. 2. Simple design for both Transmitter and Receiver. A.S.Rao
  • 41. DM Transmitter A.S.Rao
  • 42. DM Receiver Limitations / Problems of DM system •Slope over load error •Granular error (or) Hunting A.S.Rao
  • 43. Slope overload - when the analog input signal changes at a faster rate than the DAC can maintain. The slope of the analog signal is greater than the delta modulator can maintain and is called slope overload. Granular noise - It can be seen that when the original analog input signal has a relatively constant amplitude, the reconstructed signal has variations that were not present in the original signal. This is called granular noise. Granular noise in delta modulation is analogous to quantization noise in conventional PCM. A.S.Rao
  • 46. M- ary Signaling Multiple Signal Levels: Why use multiple signal levels? We can represent two levels with a single bit, 0 or 1. We can represent four levels with two bits: 00, 01, 10, 11. We can represent eight levels with three bits: 000, 001, 010, 011, 100, 101, 110, 111 Note that the number of levels is always a power of 2. M=2n A.S.Rao
  • 47. DIGITAL MODULATION Input Binary data Output Symbol/waveform A.S.Rao
  • 48. GOALS OF MODULATION TECHNIQUES • Low cost and ease of implementation • Low carrier-to-co channel interference ratio • Low-Cost/Low-Power Implementation • High Power Efficiency • High Bit Rate • High Spectral Efficiency A.S.Rao
  • 49. Bit Rate Vs Baud Rate Bit rate is the number of bits per second. Baud rate is the number of signal units (symbols) per second. Baud rate is less than or equal to the bit rate. A.S.Rao
  • 50. Modulation Units Bits/Baud Baud rate Bit Rate ASK, FSK, 2-PSK Bit 1 N N 4-PSK, 4-QAM Dibit 2 N 2N 8-PSK, 8-QAM Tribit 3 N 3N 16-QAM Quadbit 4 N 4N 32-QAM Pentabit 5 N 5N 64-QAM Hexabit 6 N 6N 128-QAM Septabit 7 N 7N 256-QAM Octabit 8 N 8N A.S.Rao
  • 52. ASK FSK A.S.Rao
  • 53. PSK A.S.Rao
  • 54. QPSK A.S.Rao
  • 55. 8 PSK A.S.Rao
  • 56. The 4-QAM and 8-QAM constellations A.S.Rao
  • 57. Time domain representation for an 8-QAM signal A.S.Rao
  • 59. Detection • Coherent Detection • Non Coherent Detection Bandwidth Efficiency Data Transmission Rate , rb  BW  M inimum Bandwidth, B 2 B TS log 2 M  BW  2 M    BW  A.S.Rao
  • 60. Matched Filter The ultimate task of a receiver is detection, i.e. deciding between 1’s and 0’s. This is done by sampling the received pulse and making a decision Matched filtering is a way to distinguish between two pulses with minimum error A.S.Rao
  • 61. Im pulse response of the Matched Filter is 2K h(t )  x(T  t ) N0 A.S.Rao
  • 64. • A sinc pulse has periodic zero crossings. If successive bits are positioned correctly, there will be no ISI at sampling instants. Sampling Instants ISI occurs but, NO ISI is present at the sampling instants A.S.Rao
  • 66. EYE DIAGRAMS The eye diagram provides visual information that can be useful in the evaluation and troubleshooting of digital transmission systems. It provides at a glance evaluation of system performance and can offer insight into the nature of channel imperfections, Top: Undistorted eye diagram of a band limited digital signal Bottom: Eye diagram includes amplitude (noise) and phase (timing) errors A.S.Rao
  • 69. Information Theory • It is a study of Communication Engineering plus Maths. • A Communication Engineer has to Fight with • Limited Power • Inevitable Background Noise • Limited Bandwidth A.S.Rao
  • 70. P varies as e  KEb e S i  Eb Rb  Eb  Si / Rb Eb   S i  or Rb   Eb  Hartley Shannon has shown that “If the rate of information from a source does not exceed the capacity of a given communication channel, then there exists a coding technique such that the information can be transmitted over the channel with arbitrary small frequency errors, despite the presence of noise.” Information theory deals with the following three basic concepts: •The measure of source information •The information capacity of a channel •Coding A.S.Rao
  • 71. Information Sources: •Analog Information Source •Discrete Information Source Information Measure Consider two Messages A Dog Bites a Man  High probability  Less information A Man Bites a Dog  Less probability  High Information Information α (1/Probability of Occurrence) The basic principle involved in determining the information content of a message is that “the information content of a message increases with its uncertainty” A.S.Rao
  • 72. Let I(mK) the information content in the Kth message. I ( mk )  0 for PK 1 I ( mk )  I ( m j ) for PK  Pj 1 I ( mk )  0 for 0  Pk  1 I (mk and m j )  I (mk m j )  I (mk )  I (m j ) 2  1  I (mk )  log b  P    k  The quantity I(mk) is called the Self information of message mk. 1 The self information convey the message is I  log P A.S.Rao
  • 73. Coding Why Coding? • to achieve reliable data communication • to achieve reliable data storage • to reduce the required transmit power • to reduce hardware costs of transmitters • to improve bandwidth efficiency • to increase channel utilisation • to increase storage density A.S.Rao
  • 74. • Source Coding • Channel Coding Source Coding • Shannon Fano Code • Huffman Code Channel Coding • Linear Block Codes •Cyclic Codes • Convolutional Codes A.S.Rao
  • 75. Shannon Fano Source code Algorithm. Step 1: Arrange all messages in descending order of probability. Step 2: Divide the Seq. in two groups in such a way that sum of probabilities in each group is same. Step 3: Assign 0 to Upper group and 1 to Lower group. Step 4: Repeat the Step 2 and 3 for Group 1 and 2 and So on…….. A.S.Rao
  • 76. Messages Pi Coding Procedure No. Of Code Mi Bits M1 ½ 0 1 0 M2 1/8/ 1 0 0 3 100 M3 1/8 1 0 1 3 101 M4 1/16 1 1 0 0 4 1100 M5 1/16 1 1 0 1 4 1101 M6 1/16 1 1 1 0 4 1110 M7 1/32 1 1 1 1 0 5 11110 m8 1/32 1 1 1 1 1 5 11111 A.S.Rao
  • 77. HUFFMAN CODING A.S.Rao
  • 78. SHANNON HARTLEY CHANNEL CAPACITY THEOREM  S C  B log 2 1    N Channel Capacity with Infinite Bandwidth C S Lt C  1.44 1.44 S B    B A.S.Rao