📄 the art of error correcting coding reed-solomon codes.htm
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<CENTER><B><FONT size=+1>Reed-Solomon codes</FONT></B></CENTER>
<P>Below are two programs written in C for simulating encoding and decoding
procedures of RS codes, which is the topic of Chapter 4 of the <FONT size=+1><A
href="http://www.amazon.com/gp/product/0470015586/ref=sr_11_1/102-3025380-7157754?ie=UTF8">book</A></FONT>.
These programs implement <I>errors-and-erasures decoding</I> with (1)
Berlekamp-Massey (BM) algorithm and (2) Euclidean algorithm for <SPAN
style="FONT-STYLE: italic">any </SPAN>shortened RS code with <SPAN
style="FONT-STYLE: italic">arbitrary starting root</SPAN> of its generator
polynomial (or starting zero of the code). </P>
<P><I>In the programs below, the Reed-Somolon code is specified by the finite
field GF(2^m), the code length (length <= 2^m-1), the number of redundant
symbols (length-k), and the initial zero of the code, init_zero.</I>
<BR><BR></P>Update 8/17/03: Added a line to check for zero in computation of the
erasure polynomial. Many thanks to Matteo Albanese, a graduate student at
Politecnico di Milano, for pointing this out!<BR>
<P><B>Encoding and errors-and-erasures decoding of an RS code, BM algorithm:</B>
<BR><A href="http://the-art-of-ecc.com/4_RS/rs_eedec_bm.c">rs_eedec_bm.c</A>
</P>Errors and erasures correction using the modified Berlekamp-Massey
algorithm. For more details and an example, see the <A
href="http://www.amazon.com/exec/obidos/ASIN/0471495816/qid=1016858656/sr=8-1/ref=sr_8_5_1/104-2054788-7703131">book</A>.
<BR><BR>See also: <A
href="http://the-art-of-ecc.com/4_RS/rs_eedec_bm_c4p3.c">rs_eedec_bm_c4p3.c</A>
and <A
href="http://the-art-of-ecc.com/4_RS/rs_eedec_bm_c4p5.c">rs_eedec_bm_c4p5.c</A><BR>
<P><B>Encoding and errors-and-erasures decoding of an RS code, Euclidean
algorithm:</B> <BR><A
href="http://the-art-of-ecc.com/4_RS/rs_eedec_euc.c">rs_eedec_euc.c</A> </P>
<P>Errors and erasures correction using the modified Euclidean algorithm. For
more details and an example, see the <A
href="http://www.amazon.com/exec/obidos/ASIN/0471495816/qid=1016858656/sr=8-1/ref=sr_8_5_1/104-2054788-7703131">book</A>.
<BR></P><A href="http://the-art-of-ecc.com/4_RS/rs_eedec_euc.c"></A><SPAN
style="FONT-WEIGHT: bold">Simulation of an RS (7,5,3) code with binary
modulation over an AWGN channel:</SPAN><BR><A
href="http://the-art-of-ecc.com/4_RS/AWGN_binRS753.m">AWGN_binRS753.m</A><BR>
<P></P><SPAN style="FONT-WEIGHT: bold">Performance of M-ary QAM over an AWGN
channel with RS coding over GF(M):</SPAN><BR><A
href="http://the-art-of-ecc.com/4_RS/rscode_AWGN_MQAM.mdl">RS coded MQAM.mdl</A>
<BR><BR>Note: This is a <SPAN style="FONT-STYLE: italic">Simulink model</SPAN>
created with Matlab version 7.1 ...<BR><BR>
<P><B><A href="http://the-art-of-ecc.com/topics.html">BACK TO CONTENTS</A></B>
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<H6><SMALL><FONT style="FONT-WEIGHT: normal" color=#000000>This page was last
updated on August 7, 2008, by Robert H.
Morelos-Zaragoza.</FONT></SMALL><BR></H6><!-- text below generated by server. PLEASE REMOVE --><!-- Counter/Statistics data collection code -->
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