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Digital communications


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Digital communications

  1. 1. A.SANYSI RAO AMIE; M.Tech; MISTE; MIETE Assoc. ProfessorBalaji 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 possibleConstraints Rules of the GAME •Limited transmit power •Limited Channel BandwidthIn 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 DigitalIt is harder to separate noise from an analog signal than it is toseparate noise from a digital signal.Noise in a digital signal. You can still discern a high voltage from a lowvoltage. A.S.Rao
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  9. 9. Bandwidth for Telephone Line A.S.Rao
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  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
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  18. 18. Core Concepts ofDigital Communications A.S.Rao
  19. 19. Elements of a Digital Communication System Source of Source Channel ModulatorInformation Encoder Encoder Binary Stream Channel Use of Source Channel DemodulatorInformation Decoder Decoder
  20. 20. Modified Diagram of a Digital Communication System From other Sources Source of Source Channel Encryptor MUX ModulatorInformation Encoder Encoder Channel Use of Source Channel DE- Decryptor DemodulatorInformation 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
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  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
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  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
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  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 nonlinearity before quantizing with a uniform quantizer.•The non linearity causes the signal amplitude to be compressed. Sothe input to the quantizer will have a more uniform distribution.•At the receiver, the signal is expanded by an inverse to thenonlinearity.•The process of compressing and expanding is called Companding. A.S.Rao
  32. 32. compression+expansion companding ˆ xx(t ) y (t ) ˆ y (t ) ˆ x(t ) x ˆ y Compress Uniform Qauntize Expand Transmitter Channel Receiver A.S.Rao
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  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 arerequired.•An increase in resolution also requires a higher number of bits persample.•The Delta Modulation is the most economical form of DigitalCommunication 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 digitaltransmission 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 Features1. 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 ReceiverLimitations / 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 fasterrate than the DAC can maintain. The slope of the analog signal isgreater than the delta modulator can maintain and is called slopeoverload.Granular noise - It can be seen that when the original analog inputsignal has a relatively constant amplitude, the reconstructed signalhas variations that were not present in the original signal. This iscalled granular noise. Granular noise in delta modulation isanalogous to quantization noise in conventional PCM. A.S.Rao
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  46. 46. M- ary SignalingMultiple 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, 111Note that the number of levels is always a power of 2. M=2n A.S.Rao
  47. 47. DIGITAL MODULATIONInput Binarydata 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 RateBit rate is the number of bits per second. Baud rate is the number ofsignal units (symbols) per second. Baud rate is less than or equal tothe bit rate. A.S.Rao
  50. 50. Modulation Units Bits/Baud Baud rate Bit RateASK, FSK, 2-PSK Bit 1 N N4-PSK, 4-QAM Dibit 2 N 2N8-PSK, 8-QAM Tribit 3 N 3N16-QAM Quadbit 4 N 4N32-QAM Pentabit 5 N 5N64-QAM Hexabit 6 N 6N128-QAM Septabit 7 N 7N256-QAM Octabit 8 N 8N A.S.Rao
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  52. 52. ASKFSK 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 DetectionBandwidth 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 FilterThe ultimate task of a receiver is detection, i.e. deciding between1’s and 0’s. This is done by sampling the received pulse andmaking a decisionMatched filtering is a way to distinguish between two pulseswith minimum error A.S.Rao
  61. 61. Im pulse response of the Matched Filter is 2Kh(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 exceedthe capacity of a given communication channel, then there existsa coding technique such that the information can be transmittedover the channel with arbitrary small frequency errors, despitethe 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 SourceInformation MeasureConsider two MessagesA Dog Bites a Man  High probability  Less informationA Man Bites a Dog  Less probability  High Information Information α (1/Probability of Occurrence)The basic principle involved in determining the informationcontent of a message is that “the information content of amessage 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. 1The 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 CodingSource Coding • Shannon Fano Code • Huffman CodeChannel Coding • Linear Block Codes •Cyclic Codes • Convolutional Codes A.S.Rao
  75. 75. Shannon Fano Source codeAlgorithm.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 BitsM1 ½ 0 1 0M2 1/8/ 1 0 0 3 100M3 1/8 1 0 1 3 101M4 1/16 1 1 0 0 4 1100M5 1/16 1 1 0 1 4 1101M6 1/16 1 1 1 0 4 1110M7 1/32 1 1 1 1 0 5 11110m8 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
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