Forward Error Correction in Computer Networks

Forward Error Correction (FEC) is a technique used to minimize errors in data transmission over communication channels. In real-time multimedia transmission, re-transmission of corrupted and lost packets is not useful because it creates an unacceptable delay in reproducing : one needs to wait until the lost or corrupted packet is resent. Thus, there must be some technique which could correct the error or reproduce the packet immediately and give the receiver the ability to correct errors without needing a reverse channel to request re-transmission of data. There are various FEC techniques designed for this purpose.

These are as follows :

1. Using Hamming Distance :
For error correction, the minimum hamming distance required to correct t errors is:
 d_m_i_n = 2t + 1

For example, if 20 errors are to be corrected then the minimum hamming distance has to be 2*20+1= 41 bits. This means, lots of redundant bits need to be sent with the data. This technique is very rarely used as we have large amount of data to be sent over the networks, and such a high redundancy cannot be afforded most of the time.

2. Using XOR :
The exclusive OR technique is quite useful as the data items can be recreated by this technique. The XOR property is used as follows –



 R= P_1\oplus P_2 \oplus .... \oplus P_i \oplus .... P_N   \rightarrow P_i = P_1 \oplus P_2 \oplus .... \oplus ...R \oplus .... P_N
If the XOR property is applied on N data items, we can recreate any of the data items P1 to PN by exclusive-Oring all of the items, replacing the one to be created by the result of the previous operation(R). In this technique, a packet is divided into N chunks, and then the exclusive OR of all the chunks is created and then, N+1 chunks are sent. If any chunk is lost or corrupted, it can be recreated at the receiver side.

Practically, if N=4, it means that 25 percent extra data has to be sent and the data can be corrected if only one out of the four chunks is lost.

3. Chunk Interleaving :
In this technique, each data packet is divided into chunks. The data is then created chunk by chunk(horizontally) but the chunks are combined into packets vertically. This is done because by doing so, each packet sent carries a chunk from several original packets. If the packet is lost, we miss only one chunk in each packet, which is normally acceptable in multimedia communication. Some small chunks are allowed to be missing at the receiver. One chunk can be afforded to be missing in each packet as all the chunks from the same packet cannot be allowed to miss.

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