Error Correction in Computer Networks

Once the errors are detected in the network, the deviated bits sequence needs to be replaced with the right bit sequence so that the receiver can accept the data and process it. This method is called Error Correction. We can correct the errors in the Network in two different ways which are listed below:

• Forward Error Correction: In this Error Correction Scenario, the receiving end is responsible for correcting the network error. There is no need for retransmission of the data from the sender’s side.

• Backward Error Correction: Backward Error Correction means that the receiver needs to correct the error either by transmitting the corrupted message or retransmitting the entire message to the destination.

However, there is one of the most widely used Error Correction methods which is called ‘Hamming Code’ which was designed by R.W.Hamming. Let us have a quick look at it.

Hamming Code Error Correction

In this method, extra parity bits are appended to the message which are used by the receiver to correct the single bit error and multiple bit error. Consider the below example to understand this method in a better way.

Suppose the sender wants to transmit the message whose bit representation is ‘1011001.’ In this message:

• Total number of bits(d) = 7

• Total of redundant bits(r) = 4 (This is because the message has four 1’s in it)

• Thus, total bits(d+r) = 7 + 4 = 11

Also, by convention, the redundant bits are always placed in the places which are powers of 2. Now, this message will take the format as shown below:

Therefore, we have R1, R2, R3, and R4 as redundant bits which will be calculated according to the following rules:

• R1 includes all the positions whose binary representation has 1 in their least significant bit. Thus, R1 covers positions 1, 3, 5, 7, 9, 11.

• R2 includes all the positions whose binary representation has 1 in the second position from the least significant bit. Thus, R2 covers positions 2,3,6,7,10,11.

• R3 includes all the positions whose binary representation has 1 in the third position from the least significant bit. Hence, R3 covers positions 4, 5, 6, 7.

• R4 includes all the positions whose binary representation has 1 in the fourth position from the least significant bit due to which R4 covers positions 8,9,10,11.

These rules are illustrated below:

Now, we calculate the value of R1, R2, R3 and R4 as follows:

• Since the total number of 1s in all the bit positions corresponding to R1 is an even number. R1 = 0.

• Since the total number of 1s in all the bit positions corresponding to R2 is an odd number, R2= 1.

• Since the total number of 1s in all the bit positions corresponding to R3 is an odd number, R3= 1.

• Since the total number of 1s in all the bit positions corresponding to R4 is even, R4 = 0.

Therefore, the message to be transmitted becomes:

This message is transmitted at the receiver’s end. Suppose, bit 6 becomes corrupted and changes to 0. Then, the message becomes ‘10101101110.’ So, at the receiver’s end, the number of 1’s in the respective bit positions of R1, R2, R3, and R4 is rechecked to correct the corrupted bit. This is done in the following steps: For all the parity bits we will check the

• For R1: bits 1, 3, 5, 7, 9, and 11 are checked. We can see that the number of 1’s in these bit positions is 4(even) so R1 = 0.

• For R2: bits 2,3,6,7,10,11 are checked. You can observe that the number of 1’s in these bit positions is 5(odd) so we get a R2 = 1.

• For R3: bits 4, 5, 6, and 7 are checked. We see that the number of 1’s in these bit positions is 3(odd). Hence, R3 = 1.

• For R8: bits 8,9,10,11 are observed. Here, the number of 1’s in these bit positions is 2 and that’s even so we get R4 = 0.

If we observe the Redundant bits, they give the binary number 0110 whose decimal representation is 6. Thus, bit 6 contains an error. To correct the error the 6th bit is changed from 1 to 0 to correct the error.

This article covers in-depth details about Errors in Networking, their types, and methods of Error Correction. By the end of this, you will gain a clear understanding of Error Correction in Computer Networking. So, let us dive deep into Error Correction in Networking.

Computer Networks play a crucial role in the secured and encrypted transmission of data over the internet. However, the data transfer over a network includes many complex processes that cause some flaws in the data transmission. These flaws are called Errors which can be of different types. Therefore, it is important to correct them for efficient data transmission.

In this article, we will learn about the different methods of Error Correction in Computer Networks. We will also see the types of errors and methods to identify them. This will resolve all your doubts about the Error Correction and its methods.