A practical guide to error-control coding using Matlab
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Error Detection and Correction
Cogent Engineering. Authors 3. Close Kilavo Hassan kilavoh nm-aist. Kisangiri Michael kisangiri. Salehe I. Mrutu smrutu gmail. Download PDF.
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References Andruszkiewicz, G. Estimating animal spirits: Conservative risk calculation. The transmitter then resends the data until they are correctly received. The second strategy, known as the forward error correction FEC , not only detects but also corrects the errors, so that data retransmission can be avoided. In many practical applications retransmission may be diffcult or not even feasible at all. For example, it is impossible for any receiver in a realtime broadcasting system to request data to be resent.
In this case, FEC is the only viable solution. Either way, error control codes ECC are used for detecting the presence of errors and correcting them. To intuitively explain the mechanism of ECC, let us look at a simple example from our daily lives. You and your friend are going for a walk. Before you leave, you recall that rain has been forecast. So you say to your friend, We should carry an umbrella with us.
Your friend may hear it as We should carry a banana with us and gets confused. However, if you instead say, We should carry an umbrella with us; its going to rain, your friend will know what you said is umbrella not banana, based on the context of your second sentence. Your second sentence in this case is redundancy that facilitates detection and correction of the error.
ECC does exactly the same thing. It frst adds redundancy to the message to be sent; this process is called encoding and is carried out at the transmitter.
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It then corrects errors based on the redundancy in a process called decoding that is performed at the receiver. The output of the encoding process is a codeword that contains both the message and the redundancy explicitly or implicitly. The redundancy is referred to as the parity check, or simply the parity.
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Figure 1. Example 1. Due to the channel error, when the bit passes the channel and arrives at the receiver it becomes a 0. Unfor-tunately there is no indication whatsoever whether the received bit is correct or not. Now, instead of sending the raw message bit, we send a codeword c formed by repeating the message bit three times.
The redundancy here is the two duplicates of the message bit. We immediately know that r is in error, because all three bits are supposed to be identical but they are not.
Notice that r differs from c0 by two bits and differs from c1 by one bit. It is logical to think that the received word is more likely to be r if c1 is sent. The two redundant bits have helped us make correct decoding.