TO ERR IS HUMAN; TO CORRECT IS MACHINE

Sometimes CD and DVD get scratched . The signal sent from satellite and space ships may be corrupted. Information sent over the INTERNET is prone to error. The mistakes that creep in 'the credit card numbers and the amount of money entered in mobiles' would be costly and dangerous. There is a technique to detect and correct errors. We will go through it with a simple example.
I want to transmit a 16 digit credit card number error free.

The number is 5196 2017 2486 8720

Transmission:

Step 1.
Split the number into 4 blocks of 4 digit each and arrange them as 4x4 matrix.

5196
2017
2486
8720

Step 2:
The sum of the digits in the first row 5+1+9+6 = 21. Throw the first digit in the sum and retain the second digit, 21 = 1. This "1" is called check-sum which plays an important role in error correcting. Find the check-sums for each row as well as each column.

5196 1
2017 0
2486 0
8720 7
7209

Step 3:
Now we have 24 digits. Rearrange them as a single line. That is, writing from left to right and from top to bottom.
519612017024860872077209
Then transmit the message.

RECEPTION

Step 1:
Receive the 24 digit message and lay them out as 5x5 matrix. There may be error in the received message.
519612014024860872077209

5196 1
2014 0
2486 0
8720 7
7209
Remember the last row and the column is check sum.

Step2:
Calculate the check sum for all the rows and columns for the received message and write them beside the received check-sums.

5196 11
2014 07
2486 00
8720 77
7209 check-sums
7206

Step 3:
If received and calculated check-sums tallies, the message is correct.

In our example check-sum of the second row and the fourth column does not tally. It pinpoints that there is error in the digit "4". From the check-sums, we understand that the difference is 3. So we make 4 into 7 and now everything tallies. So the error is detected and corrected.

We know alphabets can be represented as digits. Hence this method can also be applied to any language sentence. If the message is more than 16 digits long, it can be split into chunks of 16 digits.
This algorithm can also be applied to picture,audio,video.

Thanks for the error correction. Since we are able to enjoy HD movie on the tablet.

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