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Digital communications

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

            Assoc. Professor
Balaji Institute of Engineering...

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Transformation of Information to Signals




                       A.S.Rao

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Bandwidth




            A.S.Rao

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Digital communication unit 1
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Digital communications

  1. 1. A.SANYSI RAO AMIE; M.Tech; MISTE; MIETE Assoc. Professor Balaji Institute of Engineering & Sciences A.S.Rao
  2. 2. Transformation of Information to Signals A.S.Rao
  3. 3. Bandwidth A.S.Rao
  4. 4. Bit Rate and Bit Interval A.S.Rao
  5. 5. Corruption Due to Insufficient Bandwidth A.S.Rao
  6. 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. 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
  8. 8. A.S.Rao
  9. 9. Bandwidth for Telephone Line A.S.Rao
  10. 10. A.S.Rao
  11. 11. A.S.Rao
  12. 12. Parallel Transmission A.S.Rao
  13. 13. Serial Transmission A.S.Rao
  14. 14. Asynchronous Transmission A.S.Rao
  15. 15. Synchronous Transmission A.S.Rao
  16. 16. Ideal pulse shapes. Non ideal pulse shape. A.S.Rao
  17. 17. A.S.Rao
  18. 18. Core Concepts of Digital Communications A.S.Rao
  19. 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. 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. 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. 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. 23. PCM System A.S.Rao
  24. 24. A.S.Rao
  25. 25. A.S.Rao
  26. 26. •Quantization process •Quantization Error •Mean Square Value of Quantization Noise •SNR of PCM system A.S.Rao
  27. 27. M  S   Q.E  n   S/N   BW  A.S.Rao
  28. 28. A.S.Rao
  29. 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
  30. 30. A.S.Rao
  31. 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. 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
  33. 33. A.S.Rao
  34. 34. Telephones in US, Canada and Japan use -law Companding. (=255) A-Law is used elsewhere to compress digital telephone signals. A.S.Rao
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  37. 37. Digital Formats A.S.Rao
  38. 38. Differential PCM A.S.Rao
  39. 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. 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. 41. DM Transmitter A.S.Rao
  42. 42. DM Receiver Limitations / Problems of DM system •Slope over load error •Granular error (or) Hunting A.S.Rao
  43. 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
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  46. 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. 47. DIGITAL MODULATION Input Binary data Output Symbol/waveform A.S.Rao
  48. 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. 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. 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
  51. 51. A.S.Rao
  52. 52. ASK FSK A.S.Rao
  53. 53. PSK A.S.Rao
  54. 54. QPSK A.S.Rao
  55. 55. 8 PSK A.S.Rao
  56. 56. The 4-QAM and 8-QAM constellations A.S.Rao
  57. 57. Time domain representation for an 8-QAM signal A.S.Rao
  58. 58. 16-QAM constellations A.S.Rao
  59. 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. 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. 61. Im pulse response of the Matched Filter is 2K h(t )  x(T  t ) N0 A.S.Rao
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  63. 63. Inter Symbol Interference A.S.Rao
  64. 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
  65. 65. Raised Cosine Filter A.S.Rao
  66. 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
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  68. 68. Eye Pattern formation A.S.Rao
  69. 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. 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. 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. 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. 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. 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. 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. 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. 77. HUFFMAN CODING A.S.Rao
  78. 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
  79. 79. A.S.Rao

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