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Error correction and hamming code Subject data communication and network
Error correction  <ul><li>Error correction can be handle in two ways. </li></ul><ul><li>1)error correction by retransmissi...
Hamming code <ul><li>Hamming code can be applied to data  of any length and use the relationship b/w data and redundancy b...
<ul><li>r1 will take care of these bits </li></ul>r1 will take care of these bits r4 will take care of these bits r2 will ...
<ul><li>Example of redundancy bit calculation </li></ul><ul><li>r1=1,3,5,7,9,11 </li></ul><ul><li>r2=2,3,6,7,10,11 </li></...
Error detecting using hamming code error 11  10  9  8  7  6  5  4  3  2  1 11  10  9  8  7  6  5  4  3  2  1 11  10  9  8 ...
error 11  10  9  8  7  6  5  4  3  2  1 11  10  9  8  7  6  5  4  3  2  1 11  10  9  8  7  6  5  4  3  2  1 11  10  9  8  ...
THE END   QUSETION?
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Error Correction And Hamming Code Ibrar

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Error Correction And Hamming Code Ibrar

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  • How many redundant bits are to be sent for correcting 32 bit data unit using hamming code
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  • How to determine which redundancy bit(1,2,4,8 i.e power of two) take care of which data bits?
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Error Correction And Hamming Code Ibrar

  1. 1. Error correction and hamming code Subject data communication and network
  2. 2. Error correction <ul><li>Error correction can be handle in two ways. </li></ul><ul><li>1)error correction by retransmission: </li></ul><ul><li>When receiver detect error during transmission it request to sender to retransmit the data. </li></ul><ul><li>2)forward error correction: </li></ul><ul><li>In forward error correction code receiver use error correction code to automatically correct the data. </li></ul><ul><li>Note: error correction are more sophisticated then error detection. </li></ul>
  3. 3. Hamming code <ul><li>Hamming code can be applied to data of any length and use the relationship b/w data and redundancy bits. </li></ul><ul><li>Hamming code can find the error . </li></ul><ul><li>position of redundancy bits in hamming code </li></ul>11 10 9 8 7 6 5 4 3 2 1 r1 r2 d r4 d d d r8 d d d
  4. 4. <ul><li>r1 will take care of these bits </li></ul>r1 will take care of these bits r4 will take care of these bits r2 will take care of these bits r8 will take care of these bits 11 9 7 5 3 1 11 10 7 6 3 2 7 6 5 4 11 10 9 8 r1 r2 d r4 d d d r8 d d d r1 r2 d r4 d d d r8 d d d r1 r2 d r4 d d d r8 d d d r1 r2 d r4 d d d r8 d d d
  5. 5. <ul><li>Example of redundancy bit calculation </li></ul><ul><li>r1=1,3,5,7,9,11 </li></ul><ul><li>r2=2,3,6,7,10,11 </li></ul><ul><li>r4=4,5,6,7 </li></ul><ul><li>r8=8,9,10,11 </li></ul>Adding r1 Adding r2 Adding r4 Adding r8 Input Data 1001101 11 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1 Output data:10011100101 r1 r2 d r4 d d d r8 d d d 1 r2 1 r4 0 1 1 r8 0 0 1 1 0 1 r4 0 1 1 r8 0 0 1 1 0 1 0 0 1 1 r8 0 0 1 1 0 1 0 0 1 1 1 0 0 1
  6. 6. Error detecting using hamming code error 11 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1 r1=1 r2=1 r4=1 r8=0 8 4 2 1 0 1 1 1 7 It mean the 7 bit is corrupted example If no.1,s is even 0 If no.1,s is odd 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1
  7. 7. error 11 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1 r1=0 r2=0 r4=0 r8=1 8 4 2 1 1 0 0 0 8 It mean the 8bit is corrupted example2 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0
  8. 8. THE END QUSETION?

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