1  LINE CODING &ERROR CORRECTION        Presented By:-        Sarbjeet SIngh        NITTTR -        Chandigarh
Contents   Line coding   Reasons For Using Line Coding   Properties of a Line Code   Line coding schemes   Error Corr...
Line Coding   Line coding is always needed; which is a    technique to convert binary data to digital signal.   In the t...
Reasons For Using LineCoding   Spectrum shaping and relocation without    modulation or filtering. This is important in  ...
Cotnd..   DC component can be eliminated; this allows    AC (capacitor or transformer) coupling between    stages (as in ...
Properties of a Line Code:Self–Synchronization : There is enough timing information built into the code so that bit synchr...
Contd.. Low Probability of Bit Error : Receivers can  be  designed that will recover the binary data with  a low probabil...
Contd..   Transmission Bandwidth: This should    be as small as possible   Error Detection Capability: It should be    p...
Line coding schemes
Unipolar encoding   Unipolar encoding uses only one voltage level    ( use only one polarity +ve or -ve).
Unipolar Encoding’sProblems:Two problems: A dc component Lack of synchronization : If data contain long  sequence of 0’s...
Polar Encoding   Polar encoding uses two voltage levels (positive    and negative).   By using two levels , the average ...
NRZ: NRZ-L   The level of the signal is dependent upon the    state of the bit. A positive voltage means 0,    while nega...
NRZ: NRZ-I   In NRZ-I , the signal is inverted if a 1 is    encountered. It is the transition between a +ve and    a –ve ...
RZ encoding   To ensure synchronization, there must be a signal    change (transition) for each bit   RZ uses three valu...
Bi phase: Manchester     encoding   The transition at the middle of the bit is used for    both synchronization and bit r...
Bipolar AMI (Alternate     Mark Inversion) Encoding   Bit 0 represents by zero voltage   Bit 1s are represented by alter...
Contd..   In bipolar encoding AMI , we use three levels:    positive, zero, and negative as RZ.   Has DC component   AM...
Summary of Line Coding
Error Correction
Hamming distance   The Hamming distance between two words is    the number of differences between    corresponding bits....
Contd.. Let us find the Hamming distance between twopairs of words. The Hamming distance d(000, 011) is 2 becauseThe Ha...
Contd..   We first find all Hamming distances.   The dmin in this case is 3.
Contd..   To guarantee the detection of up to s errors    in all cases, the minimum Hamming distance    in a block code m...
Example   A code scheme has a Hamming distance    dmin = 4. What is the error detection and    correction capability of t...
LINEAR BLOCK CODES   Almost all block codes used today belong    to a subset called linear block codes.   A linear block...
Contd.. A simple parity-check code is a single-bit  error-detecting code in which  n = k + 1 with dmin = 2. Even parity ...
Simple Parity-Check Code   Table - Simple parity-check code C(5, 4)
Encoder & Decoder ForSimple Parity-Check Code
Cyclic Codes Cyclic codes are special linear block  codes with one extra property. In a cyclic code, if a codeword is cy...
A CRC code with C(7, 4)
CRC encoder and decoder
Division in CRC encoder
Division in the CRC decoderfor two cases
References   Optical fiber communications (Gerd Kesior 3rd    edition)   Data communications & networking( Behrouz    Fo...
    THANK YOU
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Line coding & error correction

  1. 1. 1 LINE CODING &ERROR CORRECTION Presented By:- Sarbjeet SIngh NITTTR - Chandigarh
  2. 2. Contents Line coding Reasons For Using Line Coding Properties of a Line Code Line coding schemes Error Correction
  3. 3. Line Coding Line coding is always needed; which is a technique to convert binary data to digital signal. In the transmission of digital information over wire or optical fiber systems, line coding (also known as modulation/data translation coding) is the method by which 1’s & 0’s are represented as transmitted waveforms.
  4. 4. Reasons For Using LineCoding Spectrum shaping and relocation without modulation or filtering. This is important in telephone line applications, e.g, where the transfer characteristic has heavy attenuation below 300 Hz. Error detection capabilities. Bandwidth usage; the possibility of transmitting at a higher rate than other schemes over the same bandwidth.
  5. 5. Cotnd.. DC component can be eliminated; this allows AC (capacitor or transformer) coupling between stages (as in telephone lines )
  6. 6. Properties of a Line Code:Self–Synchronization : There is enough timing information built into the code so that bit synchronizers can extract the timing or clock signal. A long series of binary 1’s or 0’s should not cause a problem in time recovery
  7. 7. Contd.. Low Probability of Bit Error : Receivers can be designed that will recover the binary data with a low probability of bit error when the input data is corrupted by noise or ISI. A Spectrum that is Suitable for the Channel: In addition, the signal bandwidth needs to be sufficiently small compared to the channel bandwidth, so that ISI will not be a problem.
  8. 8. Contd.. Transmission Bandwidth: This should be as small as possible Error Detection Capability: It should be possible to implement this feature easily by the addition of channel encoders and decoders, or the feature should be incorporated into the line code
  9. 9. Line coding schemes
  10. 10. Unipolar encoding Unipolar encoding uses only one voltage level ( use only one polarity +ve or -ve).
  11. 11. Unipolar Encoding’sProblems:Two problems: A dc component Lack of synchronization : If data contain long sequence of 0’s or 1’s, there is no transition in the signal during this duration that can alert the receiver to synchronization problem. The receiver receives a continuous voltage and determines how many bits are sent by relaying on its clock (bit-duration), which may not be synchronized with the sender clock.
  12. 12. Polar Encoding Polar encoding uses two voltage levels (positive and negative). By using two levels , the average voltage level is reduced and the dc component problem may be alleviated( if balance)
  13. 13. NRZ: NRZ-L The level of the signal is dependent upon the state of the bit. A positive voltage means 0, while negative means 1. Has lack of synchronization , when the data contain a long stream of 0s or 1s.
  14. 14. NRZ: NRZ-I In NRZ-I , the signal is inverted if a 1 is encountered. It is the transition between a +ve and a –ve voltage , not the voltage itself. A 0 bit is represented by no change NRZ-I is superior to NRZ-L due to synchronization each time a 1 bit is encountered.
  15. 15. RZ encoding To ensure synchronization, there must be a signal change (transition) for each bit RZ uses three values +ve, zero and –ve The signal changes during each bit A1-bit is represented by transition from +ve to zero A 0-bit by –ve to zero
  16. 16. Bi phase: Manchester encoding The transition at the middle of the bit is used for both synchronization and bit representation. It has not Dc component It achieves the same level of synchronization as RZ but with only two levels and less B-W
  17. 17. Bipolar AMI (Alternate Mark Inversion) Encoding Bit 0 represents by zero voltage Bit 1s are represented by alternating +ve and –ve voltages
  18. 18. Contd.. In bipolar encoding AMI , we use three levels: positive, zero, and negative as RZ. Has DC component AMI has a lack of synchronization when there is a stream of sequential zeros.
  19. 19. Summary of Line Coding
  20. 20. Error Correction
  21. 21. Hamming distance The Hamming distance between two words is the number of differences between corresponding bits. The minimum Hamming distance is the smallest Hamming distance between all possible pairs in a set of words.
  22. 22. Contd.. Let us find the Hamming distance between twopairs of words. The Hamming distance d(000, 011) is 2 becauseThe Hamming distance d(10101, 11110) is 3because
  23. 23. Contd.. We first find all Hamming distances. The dmin in this case is 3.
  24. 24. Contd.. To guarantee the detection of up to s errors in all cases, the minimum Hamming distance in a block code must be dmin = s + 1. To guarantee correction of up to t errors in all cases, the minimum Hamming distance in a block code must be dmin = 2t + 1.
  25. 25. Example A code scheme has a Hamming distance dmin = 4. What is the error detection and correction capability of this scheme?SolutionThis code guarantees the detection ofup to three errors (s = 3), but it cancorrect up to one error. In other words, ifthis code is used for error correction,part of its capability is wasted. Errorcorrection codes need to have an odd
  26. 26. LINEAR BLOCK CODES Almost all block codes used today belong to a subset called linear block codes. A linear block code is a code in which the exclusive OR (addition modulo-2) of two valid code words creates another valid codeword.
  27. 27. Contd.. A simple parity-check code is a single-bit error-detecting code in which n = k + 1 with dmin = 2. Even parity (ensures that a codeword has an even number of 1’s) and Odd parity (ensures that there are an odd number of 1’s in the codeword)
  28. 28. Simple Parity-Check Code Table - Simple parity-check code C(5, 4)
  29. 29. Encoder & Decoder ForSimple Parity-Check Code
  30. 30. Cyclic Codes Cyclic codes are special linear block codes with one extra property. In a cyclic code, if a codeword is cyclically shifted (rotated), the result is another codeword.
  31. 31. A CRC code with C(7, 4)
  32. 32. CRC encoder and decoder
  33. 33. Division in CRC encoder
  34. 34. Division in the CRC decoderfor two cases
  35. 35. References Optical fiber communications (Gerd Kesior 3rd edition) Data communications & networking( Behrouz Forouzan 4th edition) www.google.com
  36. 36.  THANK YOU
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