ERROR DETECTION & COORECTION

ERROR DETECTION

When a code word is transmitted, one or more of its bits may be reversed due to signal impairment. The receiver can detect these errors if the received code word is not one of the valid code word of the code set. If the corrupted received word becomes another valid code word, the error cannot be detected.

When error occurs, the distance between the transmitted and received code words is equal to the number of erroneous bits . as showing in given below figure.

TRANSMITTED CODE WORD	RECEIVED CODE WORD	NUMBER OF ERRORS	DISTANCE
11001100	11001110	1	1
10010010	00011010	2	2
10101010	10100100	3	3

In other words the valid code words must be separated by a distance more than 1 else even a single bit error will generate another valid code word and the error will not be detected. The number of errors which can be detected depends on the distance between any two valid code words. For example, if the valid code words are separated by a distance 4, upto three errors in a code word can be detected. By adding certain number of redundant bits and properly choosing the algorithm for generating them, we ensure some minimum distance between any two valid code words and, therefore, the error detection capability.

ERROR CORRECTION

After an error is detected, there are two approaches to correction of errors :

·          Reverse Error Correction (REC).

·          Forward Error Correction (FFC).

In the first approach, the receiver requests for retransmission of the code word. In the second approach, the code set is so designed that it is possible for the receiver to not only detect but correct the errors also without requesting for retransmission. The receiver either locates the errors by analysing the received code word and reverses the erroneous bits. An alternative way is to search the most likely correct code word. When an error is detected, the distances of all the valid code words from the received invalid code word are measured. The nearest valid code word is the most likely correct version of the received word (Fig.3). If the minimum distance between valid code words is D, upto D/2-1 errors can be corrected. More than D/2-1 errors will cause the received code word to be nearer to the wrong valid code word.