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<span class="fxxl"><b>dvdisaster</b></span>
<i>Version 0.72.4 / 0.72 (pl4)</i>
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<span class="fxxl"> </span><a href="http://dvdisaster.net/en/">To the Internet version</a>
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<span class="fs"><b>Contents</b></span>
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<tr><td colspan=3><span class="fs"><a href="index.html">Overview</a></span></td></tr>
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<tr><td style="width:1%; vertical-align:top;">·</td><td colspan=2><span class="fs"><a href="howtos60.html">The big picture</a></span></td></tr>
<tr><td></td><td style="vertical-align:top; font-size:small;">-</td><td><span class="fs">error correction</span></td></tr>
<tr><td></td><td style="vertical-align:top; font-size:small;">-</td><td><span class="fs"><a href="howtos62.html">correct usage</a></span></td></tr>
<tr><td></td><td style="vertical-align:top; font-size:small;">-</td><td><span class="fs"><a href="howtos63.html">incorrect usage</a></span></td></tr>
<tr><td style="width:1%; vertical-align:top;">·</td><td colspan=2><span class="fs"><a href="howtos10.html">Scanning media for errors</a></span></td></tr>
<tr><td style="width:1%; vertical-align:top;">·</td><td colspan=2><span class="fs"><a href="howtos20.html">Putting error correction data on a separate file</a></span></td></tr>
<tr><td style="width:1%; vertical-align:top;">·</td><td colspan=2><span class="fs"><a href="howtos30.html">Putting error correction data on the medium</a></span></td></tr>
<tr><td style="width:1%; vertical-align:top;">·</td><td colspan=2><span class="fs"><a href="howtos40.html">Recovering media images</a></span></td></tr>
<tr><td style="width:1%; vertical-align:top;">·</td><td colspan=2><span class="fs"><a href="howtos50.html">Getting information about images and error correction data</a></span></td></tr>
<tr><td style="width:1%; vertical-align:top;">·</td><td colspan=2><span class="fs"><a href="howtos90.html">Testing image compatibility</a></span></td></tr>
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<h3 class="top">The idea behind the error correction</h3>
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<td><img src="../images/bad-cd.png" alt="Icon: Damaged medium (partially unreadable)"></td>
<td> </td>
<td><img src="../images/ecc.png" alt="Icon: Separate file with error correction data"></td>
<td> </td>
<td rowspan="3">
The example from the previous page told us how dvdisaster reconstructs
data by using the still readable parts of the medium together with
the error correction data.<p>
In order to get the most out of dvdisaster a basic understanding
of the error correction method is helpful. And while we are at it we
can refute a misunderstanding we sometimes hear - the error correction
data is <b>not</b> simply a copy of the last 20% data sectors.
That'd really be a cheap shot ;-)
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<td align="right" class="w65x">80%<img src="../images/rdiag-arrow.png" alt="Icon: Diagonal arrow right"></td>
<td> </td>
<td align="left" class="w65x"><img src="../images/ldiag-arrow.png" alt="Icon: Diagonal arrow left">20%</td>
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<td> <img src="../images/good-image.png" alt="Icon: Complete image"></td>
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</table><p>
<b>Example: Anna's desk drawer PIN</b><p>
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:<p>
<img src="../images/ecc-example1.png" alt="8 6 2 3"><p>
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):<p>
<img src="../images/ecc-example2.png" alt="8+6+2+3=19"><p>
After a while one of the numbers indeed gets covered by an ink spot:<p>
<img src="../images/ecc-example3.png" alt="8+ +6+2+3=19"><p>
But this is not a problem as Anna can re-calculate the missing
number <i>x</i>
by rearranging the still readable parts of the equation:<p>
8 + x + 2 + 3 = 19, hence<p>
x = 19 - 8 - 2 - 3, and therefore x = 6.<p>
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:
<p>
<table><tr><td><img src="../images/ecc-example4.png" alt="8+6+2+3 (medium)=19 (ecc)"></td><td> </td>
<td class="valignt">
For a given set of data (e.g. the numbers "8 6 2 3")
additional error correction data (e.g. the sum "19") can be created
so that a lost datum can be re-calculated from the remaining data.<p>
The same principle is used in dvdisaster; the protected sequence of numbers
is nothing else than the ISO image of a CD, DVD or BD.</td>
</tr></table><p>
The concept of <b>redundancy</b> can be explained as follows:
<ul>
<li>One "error correction number" is calculated for four input numbers.
1 of 4 (or 1/4) relates to a redundancy of 25%.</li>
<li> From one error correction number we can re-calculate exactly one missing
number, or at most 25% of data.
The redundancy is equivalent to the maximum capacity of the error correction.</li>
<li> Additional storage required for the error correction data is also
determined by the redundancy (25% in the example).</li>
</ul>
dvdisaster uses the term of redundancy accordingly. In addition please
observe that
<ul>
<li>no data can be recovered when the data loss exceeds the redundancy
(the equation in the example can not be solved for two or more unknowns).</li>
<li>the error correction data must be calculated at a point in time
where all data is still present / readable.</li>
</ul><p>
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.
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<span class="fs">
<i> Copyright 2004-2012 Carsten Gnörlich.<br>
Verbatim copying and distribution of this entire article is permitted in any medium, provided this notice is preserved.
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