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<HTML><HEAD><TITLE> References on Low Density Parity Check Codes </TITLE></HEAD><BODY><H1> References on Low Density Parity Check Codes </H1>Robert Gallager's original work on low density parity check codes was publishedas the following book, based his doctoral dissertation, and a related paper:<BLOCKQUOTE><P>Gallager, R. G. (1963) <I>Low Density Parity Check Codes</I>, Cambridge, MA: MIT Press.<P>Gallager, R. G. (1962) ``Low-density parity-check codes'', <I>IRE Transactions on Information Theory</I>, vol. IT-8, pp. 21-28.</BLOCKQUOTE>More recent work on these codes by David MacKay and myself was publishedas follows:<BLOCKQUOTE><P>MacKay, D. J. C. and Neal, R. M. (1996) ``Near Shannon limit performance of low density parity check codes'', <I>Electronics Letters</I>, vol. 32, pp. 1645-1646. Reprinted with printing errors corrected in vol. 33, pp. 457-458.<P>MacKay, D. J. C. (1999) ``Good error-correcting codes based on very sparse matrices'', <I>IEEE Transactions on Information Theory</I>, vol. 45, pp. 399-431.</BLOCKQUOTE>The decoding algorithms described in the above references can visualizedin terms of a ``factor graph'' representation of the code, as describedin the following paper:<BLOCKQUOTE><P>Kschischang, F. R., Frey, B. J., and Loeliger, H.-A. (1998) ``Factor graphs and the sum-product algorithm'', available from <A HREF="http://www.cs.toronto.edu/~frey/papers/fgspa.abs.html">here</A>.</BLOCKQUOTE>I presented the application of sparse matrix techniques to encoding ofLDPC codes at the IMA workshop on Codes, Systems and Graphical Models,Minneapolis, 1999. You can view the slides of this talk as <AHREF="sparse-encode.ps.gz">Postscript</A> or <AHREF="sparse-encode.pdf">PDF</A>. <B>Note</B>: Due to a bug in theprogram I used then, the results shown for the minimal product heuristic inthese slides are somewhat worse than the actual performance. For instance,the number of bit operations per check bit for for <I>M</I>=3200 with3 checks per bit is actually around 12.7, not the value around 17 shownon one of the slides.<P>Text and references to many more recent and classical papers can beobtained via the <A HREF="http://www.ima.umn.edu/csg/">IMA workshop'sweb page</A>.<HR><A HREF="index.html">Back to index for LDPC software</A></BODY></HTML>?? 快捷鍵說明
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