dvdisaster Version 0.72.6 / 0.79 (devel-3) | To the Internet version |
The idea behind the error correction
Example: Anna's desk drawer PIN Anna has got a desk whose drawers can only be opened after entering the numbers "8 6 2 3" into a code lock. Since the drawers do not contain any sensitive information she decides to note down the numbers directly on the desktop:
Anna is cautious and expects one of the numbers to become unreadable by accidentally pouring ink over it. Therefore she also notes down the sum of the four numbers (the "+" and "=" signs have only be added for clarity):
After a while one of the numbers indeed gets covered by an ink spot:
But this is not a problem as Anna can re-calculate the missing number x by rearranging the still readable parts of the equation: 8 + x + 2 + 3 = 19, hence x = 19 - 8 - 2 - 3, and therefore x = 6. It is easily seen that any one of the original five numbers can be recovered from the remaining four. The example also demonstrates some important properties of the error correction:
The concept of redundancy can be explained as follows:
The above shown example does not generalize into an error correction scheme for recovering more than one missing data value. To do so a more powerful equation system is needed which can be solved for more than one missing value. dvdisaster uses a Reed-Solomon code which does have such properties; however the required math is not taught in school. Interested readers are therefore referred to the respective books in coding theory. |
Copyright 2004-2014 Carsten Gnörlich. Verbatim copying and distribution of this entire article is permitted in any medium, provided this notice is preserved. |
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