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Line coding & error correction



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  • 1. 1 LINE CODING &ERROR CORRECTION Presented By:- Sarbjeet SIngh NITTTR - Chandigarh
  • 2. Contents Line coding Reasons For Using Line Coding Properties of a Line Code Line coding schemes Error Correction
  • 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. 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. Cotnd.. DC component can be eliminated; this allows AC (capacitor or transformer) coupling between stages (as in telephone lines )
  • 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. 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. 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. Line coding schemes
  • 10. Unipolar encoding Unipolar encoding uses only one voltage level ( use only one polarity +ve or -ve).
  • 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. 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. 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. 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. 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. 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. Bipolar AMI (Alternate Mark Inversion) Encoding Bit 0 represents by zero voltage Bit 1s are represented by alternating +ve and –ve voltages
  • 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. Summary of Line Coding
  • 20. Error Correction
  • 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. 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. Contd.. We first find all Hamming distances. The dmin in this case is 3.
  • 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. 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. 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. 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. Simple Parity-Check Code Table - Simple parity-check code C(5, 4)
  • 29. Encoder & Decoder ForSimple Parity-Check Code
  • 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. A CRC code with C(7, 4)
  • 32. CRC encoder and decoder
  • 33. Division in CRC encoder
  • 34. Division in the CRC decoderfor two cases
  • 35. References Optical fiber communications (Gerd Kesior 3rd edition) Data communications & networking( Behrouz Forouzan 4th edition)
  • 36.  THANK YOU