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CS412 Introduction to Computer Networking & Telecommunication

CS412 Introduction to Computer Networking & Telecommunication. Error Correction/Detection. Topics. Introduction Error Correction Error Detection. Introduction. Transmission impairments (errors) Attenuation Loss of energy as signal propagates Delay Distortion

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CS412 Introduction to Computer Networking & Telecommunication

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  1. CS412 Introduction to Computer Networking & Telecommunication Error Correction/Detection Chi-Cheng Lin, Winona State University

  2. Topics • Introduction • Error Correction • Error Detection

  3. Introduction • Transmission impairments (errors) • Attenuation • Loss of energy as signal propagates • Delay Distortion • Components travel at different speeds • Noise • Unwanted energy from other sources

  4. Figure 3.21Attenuation

  5. Figure 3.23Distortion

  6. Figure 3.24Noise

  7. Isolated and Burst Error • Isolated: 0 -> 1, or 1 -> 0 • Burst: errors in consecutive bits • 2 or more bits in the data unit have changed

  8. Isolated and Burst Error • Compare burst errors to isolated errors • Fewer error blocks given a fixed error rate • Example: error rate: 0.001 per bit (1 error out of 1000 bits) block size: 1000 bits burst size: 100 isolated error: an error contained in most blocks burst error: 1 or 2 error blocks out of 100 blocks • Error correction/detection much harder

  9. Error Correcting/Detecting Codes • Redundancy added to data • Error correction • Referred to as forward error correction • Detect and correct error • Error detection • Detect error and request retransmission • Codeword (n bits) • data + redundancy (m bits) (r bits) • n = m + r When to use which one?

  10. 10.3Redundancy

  11. Error Correction • Hamming Code • For m-bit data we need r-bit redundancy, where (m+r+1)  2r • Redundancy bits are placed in position of 2’s power • Example: If m = 7, then r = 4

  12. 10.15Redundancy bits calculation

  13. 10.16Example of redundancy bit calculation

  14. 10.17Error detection using Hamming code

  15. Correct Burst Errors • Organize k codewords into a (k x n) matrix • (k x r) check bits for (k x m) data • Transmit one column at a time • Reconstruct matrix after received • Correct burst errors of length k

  16. Correct Burst Errors n m k

  17. 10.18Burst error correction example

  18. Error Detection • Parity bit • Error detection • Added to data so that number of 1 bits in codeword is • Even (even parity) • Odd (odd parity) • E.g., ASCII of ‘H’ is 1001000, its codeword is • ________ if even parity is used • ________ if odd parity is used 01001000 11001000

  19. 10.5Even-parity concept

  20. Error Detection vs. Correction • Error-detecting and retransmission • More efficient than error-correction when error rate is low • Example: • error rate: 0.000001 per bit block size: 1000 bits check bits per block: Hamming code error correction: 10 Parity code error detection: 1 overhead for 1M data: e. c. 10000 bits e. d. 2001 bits

  21. Use Parity to Detect Burst Errors • Organize a block into (k x n) matrix • One parity for each column  one row of parities at the bottom • Transmit one row at a time • Can detect burst errors of length n

  22. Example Original data 11100111 11011101 00111001 10101001 Organized into 11100111 11011101 00111001 10101001 10101010  LRC Transmitted 11100111 11011101 00111001 10101001 10101010 Burst error 11100111 11010000 01001001 10101001 10101010 Error detected  whole block is discarded 11100111 11010000 0100001 10101001 10101010

  23. Error-Detecting Code - CRC • Bit stream is treated as polynomial w/ coefficients 0 and 1 • Example: • data: 10100111 polynomial: degree = 7 • Modulo 2 arithmetic is used • Example: 10011011 11110000 +11001010 -10100110 01010001 01010110 • XOR

  24. Error-Detecting Code - CRC • Use generator polynomial G(x) to calculate checksum • Frame: P(x) generator: G(x) degree of G(x) = d Transmitted: checksummed frame P(x)·xd + R(x) • It’s guaranteed that P(x)·xd + R(x) is divisible by G(x)!!

  25. Error-Detecting Code - CRC • Receiver divides checksummed frame by G(x) • If remainder is zero • No error, CRC is removed • Otherwise • Error, the frame is discarded

  26. 10.8Binary division in a CRC generator • Frame: • Generator: • Frame transmitted: 100100001

  27. 10.9Binary division in CRC checker

  28. CRC - Example 1 1 0 0 0 0 • Frame: • Generator:

  29. CRC Properties • Single error detection • Double error detection w/ carefully chosen G(x) • Odd number error detection if (x + 1) is a factor of G(x) • Detect burst error length  r for r check bits • Can be implemented in hardware using simple shift register circuit

  30. Table 10.1 Standard polynomials

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