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59 lines
2.2 KiB
HTML
59 lines
2.2 KiB
HTML
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<TITLE> References on Low Density Parity Check Codes </TITLE>
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<H1> References on Low Density Parity Check Codes </H1>
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Robert Gallager's original work on low density parity check codes was published
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as the following book, based his doctoral dissertation, and a related paper:
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<BLOCKQUOTE>
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<P>Gallager, R. G. (1963) <I>Low Density Parity Check Codes</I>,
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Cambridge, MA: MIT Press.
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<P>Gallager, R. G. (1962) ``Low-density parity-check codes'', <I>IRE
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Transactions on Information Theory</I>, vol. IT-8, pp. 21-28.
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</BLOCKQUOTE>
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More recent work on these codes by David MacKay and myself was published
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as follows:
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<BLOCKQUOTE>
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<P>MacKay, D. J. C. and Neal, R. M. (1996) ``Near Shannon limit performance
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of low density parity check codes'', <I>Electronics Letters</I>,
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vol. 32, pp. 1645-1646. Reprinted with printing errors corrected
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in vol. 33, pp. 457-458.
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<P>MacKay, D. J. C. (1999) ``Good error-correcting codes based on very
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sparse matrices'', <I>IEEE Transactions on Information Theory</I>,
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vol. 45, pp. 399-431.
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</BLOCKQUOTE>
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The decoding algorithms described in the above references can visualized
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in terms of a ``factor graph'' representation of the code, as described
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in the following paper:
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<BLOCKQUOTE>
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<P>Kschischang, F. R., Frey, B. J., and Loeliger, H.-A. (1998) ``Factor graphs
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and the sum-product algorithm'', <I>IEEE Transactions on Information
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Theory</I>, vol. 47, pp. 498-519.
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</BLOCKQUOTE>
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I presented the application of sparse matrix techniques to encoding of
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LDPC codes at the IMA workshop on Codes, Systems and Graphical Models,
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Minneapolis, 1999. You can view the slides of this talk <A
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HREF="sparse-encode.pdf">here</A>. <B>Note</B>: Due to a bug in the
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program I used then, the results shown for the minimal product heuristic in
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these slides are somewhat worse than the actual performance. For instance,
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the number of bit operations per check bit for for <I>M</I>=3200 with
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3 checks per bit is actually around 12.7, not the value around 17 shown
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on one of the slides.
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<P>Text and references to many more recent and classical papers can be
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obtained via the <A HREF="http://www.ima.umn.edu/csg/">IMA workshop's
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web page</A>.
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<HR>
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<A HREF="index.html">Back to index for LDPC software</A>
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</BODY></HTML>
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