# ERROR CORRECTION

Error Correction means rectifying all the bits that have been altered or changed during the transmission of data.

Error Correction can be done in two ways:

§  By Retransmission of data from sender to receiver

§  By the use of error correction codes at the receiving state.

Error Correction Method:

§  Hamming Code is a technique developed by R.W. Hamming for error connection.

§  This method corrects the error by finding the state at which the error has occurred.

§  To determine the position of error bits, redundant bits are added to the data unit.

§  A single addition bit can detect single bit errors but to correct a single bit error or burst error.

§  The error correction code must determine which of the seven bits has changed.  §  To calculate the number of redundancy bits require to correct a given number of data unit, there is a relationship between M and R.

§  If there are M data units, then there should be R redundancy bits and the length of the resulting code is M+R.

§  To calculate the r, there is a formula as 2 the power r >= m+r+1

§  After determining the total required redundancy bits now, we have to determine the number of position at which these redundancy bits will be placed within the data unit.

§  For example: In case of seven bit data four redundancy bits are required and the redundancy bits will be placed at position 1, 2, 4, 8.

§  To find the value of these redundancy bits, we have to check all that bit position which is taken care by these redundancy bits.  §  The data bits taken care by r1 are 1,3,5,7,9,11.

§  The data bits taken care by r2 are 2,3,6,7,10,11.

§  The data bits taken care by r4 are 4,5,6,7.

§  The data bits taken care by r8 are 8,9,10,11.  §  For determining the value of r1 , r2, r4, r8, we will check the even parity for all these redundancy bits.

§  For example: Suppose a binary number 1001101 is to be transmitted.

§  To implement hamming code for this follow these steps:

·         Calculate the number of redundancy bits required with the formula 2 the power r >= m+r+1 that 2 the power 4 >= 7+4+1.Therefore number of redundancy bits =4.

·         Determining the position of various data bits and redundancy bits. The various r bits are replaced at the position that corresponds to power of 2 that 1,2,4,8.

·         Determining the value of r1, r2, r4,r8 with even parity system. r1 is VRC for bit no 1,3,5,7,9,11.
r1= r1, 1,0,1,0,1.
So the value of r1=1.
rest is same as above written.

·         Considering a case if bit number 10 has been changed, then we will check the even parity for r1,r2,r4,r8. We find that, there is a problem in r2 bit and r8 bit, So we can find the incorrect bit by adding 8+2=10. 10th position bit is not correct.