Error correction techniques include retransmission of data when errors are detected and forward error correction where error correction codes are used to automatically correct errors. Hamming codes can detect and correct errors by using redundancy bits in the data and calculating parity checks to determine the position of errors. The document provides an example of how hamming codes work by adding redundancy bits to input data and using the parity checks to detect errors in the encoded data.

1. Error correction and hamming code Subject data communication and network

2. Error correction Error correction can be handle in two ways. 1)error correction by retransmission: When receiver detect error during transmission it request to sender to retransmit the data. 2)forward error correction: In forward error correction code receiver use error correction code to automatically correct the data. Note: error correction are more sophisticated then error detection.

3. Hamming code Hamming code can be applied to data of any length and use the relationship b/w data and redundancy bits. Hamming code can find the error . position of redundancy bits in hamming code 11 10 9 8 7 6 5 4 3 2 1 r1 r2 d r4 d d d r8 d d d

4. r1 will take care of these bits 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. Example of redundancy bit calculation r1=1,3,5,7,9,11 r2=2,3,6,7,10,11 r4=4,5,6,7 r8=8,9,10,11 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. 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. 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. THE END QUSETION?