📄 the art of error correcting coding cyclic codes and bch codes.htm
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<CENTER><B><FONT size=+1>Binary Cyclic Codes and BCH codes</FONT></B></CENTER>
<P>Below are links to several programs written in C, and Matlab scripts, for
simulating encoding/decoding procedures and analyzing binary cyclic codes
and binary BCH codes, the topic of Chapter 3 of the <A
href="http://www.amazon.com/gp/product/0470015586/ref=sr_11_1/102-3025380-7157754?ie=UTF8">book!</A>
<BR> </P>
<P><B>Encoding and decoding of a shortened cyclic code:</B> <BR><A
href="http://the-art-of-ecc.com/3_Cyclic_BCH/RBDS.c">RBDS.c</A> </P>The decoding
algorithm used in RBDS.c is based on error trapping. The program emulates the
operation of the encoder and decoder of a binary cyclic codes, using bitwise
shifts and xor for modulo g(x) operations.<BR><BR><BR><SPAN
style="FONT-WEIGHT: bold">Illustration of a PGZ errors-only decoder of a binary
primitive BCH code:</SPAN><BR><A
href="http://the-art-of-ecc.com/3_Cyclic_BCH/bch_example.m">bch_example.m</A><BR><BR
style="FONT-WEIGHT: bold"><SPAN style="FONT-WEIGHT: bold">Compute the generator
polynomial of a binary Euclidean geometry (EG) code:</SPAN><BR><A
href="http://the-art-of-ecc.com/3_Cyclic_BCH/egcodepol.m">egcodepol.m</A><BR><BR><SPAN
style="FONT-WEIGHT: bold">Compute the generator polynomial of a binary
projective geometry (PG) code:</SPAN><BR><A
href="http://the-art-of-ecc.com/3_Cyclic_BCH/pgcodepol.m">pgcodepol.m</A><BR><BR><SPAN
style="FONT-WEIGHT: bold">Compute the generator polynomial of a binary BCH
(15,5,7) code:</SPAN><BR><A
href="http://the-art-of-ecc.com/3_Cyclic_BCH/genpol_bch_150507.m">genpol_bch_150507.m</A>
<BR><BR>
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<P><SMALL><I>NOTE: For the BCH decoders in C language below and the RS decoders
in another section, log and antilog tables are used to solve equations for the
unkown error positions (and values for RS codes). The value "-1" in the log
table indicates log(0) or "-infinity". Therefore, the programs have a number of
testing conditions for this value, when multiplying two elements in the Galois
field.</I> </SMALL><BR> </P>
<P><B>Encoding and decoding of a shortened binary (48,36,5) BCH code:</B> <BR><A
href="http://the-art-of-ecc.com/3_Cyclic_BCH/bch4836.c">bch4836.c</A> </P>
<P>Application of the PGZ decoding algorithm for t=2. <BR> </P>
<P><B>Encoding and decoding of binary BCH codes with the Berlekamp-Massey
decoding algorithm:</B> <BR><A
href="http://the-art-of-ecc.com/3_Cyclic_BCH/bch_bm.c">bch_bm.c</A> </P>
<P>Uses the Berlekamp-Massey decoding algorithm. Any (valid) code length can be
input. <BR> </P>
<P><B>Encoding and decoding of binary BCH codes with the Euclidean
algorithm:</B> <BR><A
href="http://the-art-of-ecc.com/3_Cyclic_BCH/bch_euc.c">bch_euc.c</A> </P>
<P>Decoding with the Euclidean algorithm. Any (valid) code length can be input.
<BR> </P>
<P><B>Simulation of a BCH code with binary transmission over an AWGN channel.
Berlekamp-Massey algorithm:</B> <BR><A
href="http://the-art-of-ecc.com/3_Cyclic_BCH/bch_awgn.c">bch_awgn.c</A> </P>
<P>Shows how to incorporate the AWGN/Rayleigh fading models in a basic decoding
program. <BR> </P>
<P><B>Encoding and errors-and-erasures decoding of binary BCH codes with the
Euclidean algorithm:</B> <BR><A
href="http://the-art-of-ecc.com/3_Cyclic_BCH/bch_erasures.c">bch_erasures.c</A>
</P>
<P>Erasure correction achieved by two errors-only decoding passes using the
Euclidean algorithm. Any (valid) code length can be input. <BR> </P>
<P><B><A href="http://the-art-of-ecc.com/topics.html">BACK TO CONTENTS</A></B>
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<H6 style="FONT-WEIGHT: normal"><SMALL><FONT color=#000000>This page was last
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