132 lines
4.2 KiB
PHP
132 lines
4.2 KiB
PHP
<?php
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# dvdisaster: English homepage translation
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# Copyright (C) 2004-2010 Carsten Gnörlich
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#
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# UTF-8 trigger: äöüß
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#
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# Include our PHP sub routines, then call begin_page()
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# to start the HTML page, insert the header,
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# navigation and news if appropriate.
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require("../include/dvdisaster.php");
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begin_page();
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?>
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<!--- Insert actual page content below --->
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<h3>The idea behind the error correction</h3>
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<table width="100%">
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<tr valign="top">
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<td><img src="../images/bad-cd.png"></td>
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<td> </td>
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<td><img src="../images/ecc.png"></td>
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<td> </td>
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<td rowspan="3">
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The example from the previous page told us how dvdisaster reconstructs
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data by using the still readable parts of the medium together with
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the error correction data.<p>
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In order to get the most out of dvdisaster a basic understanding
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of the error correction method is helpful. And while we are at it we
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can refute a misunderstanding we sometimes hear - the error correction
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data is <b>not</b> simply a copy of the last 20% data sectors.
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That'd really be a cheap shot ;-)
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</td>
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</tr>
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<tr>
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<td align="right">80%<img src="../images/rdiag-arrow.png"></td>
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<td> </td>
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<td align="left"><img src="../images/ldiag-arrow.png">20%</td>
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<td> </td>
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</tr>
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<tr>
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<td> </td>
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<td> <img src="../images/good-image.png"></td>
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<td> </td>
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<td> </td>
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</tr>
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</table><p>
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<b>Example: Anna's desk drawer PIN</b><p>
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Anna has got a desk whose drawers can only be opened after entering
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the numbers "8 6 2 3" into a code lock. Since the drawers do not contain
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any sensitive information she decides to note down the numbers directly
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on the desktop:<p>
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<img src="../images/ecc-example1.png"><p>
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Anna is cautious and expects one of the numbers to become unreadable
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by accidentally pouring ink over it. Therefore she also notes down
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the sum of the four numbers (the "+" and "=" signs have only be added for
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clarity):<p>
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<img src="../images/ecc-example2.png"><p>
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After a while one of the numbers indeed gets covered by an ink spot:<p>
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<img src="../images/ecc-example3.png"><p>
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But this is not a problem as Anna can re-calculate the missing
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number <i>x</i>
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by rearranging the still readable parts of the equation:<p>
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8 + x + 2 + 3 = 19, hence<p>
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x = 19 - 8 - 2 - 3, and therefore x = 6.<p>
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It is easily seen that any one of the original five numbers can be
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recovered from the remaining four. The example also demonstrates
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some important properties of the error correction:
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<p>
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<table><tr><td><img src="../images/ecc-example4.png"></td><td> </td>
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<td valign="top">
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For a given set of data (e.g. the numbers "8 6 2 3")
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additional error correction data (e.g. the sum "19") can be created
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so that a lost datum can be re-calculated from the remaining data.<p>
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The same principle is used in dvdisaster; the protected sequence of numbers
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is nothing else than the ISO image of a CD, DVD or BD.</td>
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</tr></table><p>
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The concept of <b>redundancy</b> can be explained as follows:
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<ul>
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<li>One "error correction number" is calculated for four input numbers.
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1 of 4 (or 1/4) relates to a redundancy of 25%.</li>
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<li> From one error correction number we can re-calculate exactly one missing
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number, or at most 25% of data.
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The redundancy is equivalent to the maximum capacity of the error correction.</li>
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<li> Additional storage required for the error correction data is also
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determined by the redundancy (25% in the example).</li>
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</ul>
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dvdisaster uses the term of redundancy accordingly. In addition please
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observe that
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<ul>
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<li>no data can be recovered when the data loss exceeds the redundancy
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(the equation in the example can not be solved for two or more unknowns).</li>
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<li>the error correction data must be calculated at a point in time
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where all data is still present / readable.</li>
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</ul><p>
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The above shown example does not generalize into an error correction
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scheme for recovering more than one missing data value. To do so a more
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powerful equation system is needed which can be solved for more than
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one missing value. dvdisaster uses a Reed-Solomon code
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which does have such properties; however the required math is not taught
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in school. Interested readers are therefore referred to the respective
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books in coding theory.
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<!--- do not change below --->
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<?php
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# end_page() adds the footer line and closes the HTML properly.
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end_page();
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?>
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