DATA COMMUNICATIONS & NETWORKING

LECTURE-22

Course Instructor : Sehrish Rafiq

Department Of Computer Science

University Of Peshawar

ERROR CORRECTION

ERROR CORRECTION

The two most common error correction ways are

Error correction by retransmission In this technique when an error is

discovered,the receiver can have the sender retransmit the entire data unit.

Forward error correction In forward error correction a receiver can use

an error-correcting code, which automatically corrects certain errors.

ERROR CORRECTION

Error-correcting codes however are more sophisticated than error detection codes and require more redundancy bits.

A single additional bit can detect single bit errors in any sequence of bits because it must distinguish only between two conditions :error or no error.

ERROR CORRECTION

However to correct a single bit error in ASCII character, the error correction code must determine which of the seven bits have changed.

In this case we have to distinguish between eight different states :no error, error in position 1,error in position 2, and so on.

RELATIONSHIP BETWEEN DATA AND REDUNDANCY BITS

To calculate the number of redundancy bits r required to correct a given number of data bits m the following formula can be used:

2r >=m+r+1

RELATIONSHIP BETWEEN DATA AND REDUNDANCY BITS

Number ofdata bits

m

Number of redundancy bits

r

Total bits

m + r

11 2 3

22 3 5

33 3 6

44 3 7

55 4 9

66 4 10

77 4 11

HAMMING CODE

The hamming code can be applied to data units of any length and uses the relationship between data and redundancy bits discussed above.

HAMMING CODE

In Hamming code, each r bit is the parity bit for one combination of data bits as shown below:

r1: bits 1,3,5,7,9,11 r2: bits 2,3,6,7,10,11 r4: bits 4,5,6,7 r8: bits 8,9,10,11 Note: In the sequence above each of the

original data bits is included in at least two sets while the r bits are included only once.

REDUNDANCY BIT CALCULATION

EXAMPLE OF REDUNDANCY BIT CALCULATION

ERROR DETECTION USING HAMMING CODE

BURST ERROR CORRECTION

Although the hamming code cannot correct a burst error directly, it is possible to rearrange the data and then apply the code.

Instead of sending all the bits in data unit together, we can organize N units in a column and then the first bit of each , followed by the second bit of each and so on.

BURST ERROR CORRECTION CONT…

In this way if an error of M bits occurs (M<N), then the error does not corrupt M bits of one single unit,it corrupts only one bit of a unit.

With the Hamming code we can correct the corrupted bit in each unit.

BURST ERROR CORRECTION EXAMPLE

THANKS!!!