In , a decoding algorithm for errors and erasures for Reed-Solomon
codes is briefly stated. The algorithm uses the Massey-Berlekamp
algorithm to find the error-locators, and Forney's algorithm to find
the values of the errors and erasures.
However, the decoding algorithm is for the Reed-Solomon codes
generated by g(x) = (x - a^1)(x - a^2)...(x - a^[n-k]). How should I
adapt Forney's algorithm when I want to use the generator polynomial
(x - a^0)(x - a^1)...(x - a^[n-k-1])?
Your time, effort and suggestions will be highly appreciated
 S.B. Wicker and V.K. Bhargava, Reed-Solomon codes and their
applications. New York: Institute of Electrical and Electronic
Engineers, Inc., 1994.
Reply by ●February 11, 20052005-02-11
I had a similar problem while writing a RS decoder a while back.
There are two things that you need to take caree of:
1. Syndrome computation should be modified to compute at roots alpha^i,
2. The forney algorithm should be computed using the relation
where m is the lowest root of the RS generator polynomial. I need to
look back at my code to verify that this expression is absolutely
correct [I was succesfully able to get my code to work for arbitrary
start powers of the roots of the gen poly].
Finally, the book "The Art of Error correction coding" by Robert
Morelos Zaragoza has some very relavent information in this very topic.
Hope that helps,
Reply by ●February 14, 20052005-02-14
"Jaco Versfeld" <email@example.com> asked in message
> How should I
> adapt Forney's algorithm when I want to use the generator polynomial
> (x - a^0)(x - a^1)...(x - a^[n-k-1])?