Hi, In [1], 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 Jaco [1] S.B. Wicker and V.K. Bhargava, Reed-Solomon codes and their applications. New York: Institute of Electrical and Electronic Engineers, Inc., 1994.

# Reed-Solomon decoding: Using different gen. polynomials.

Started by ●February 11, 2005

Reply by ●February 11, 20052005-02-11

Dear Jaco, 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, i=0..2*t-1. 2. The forney algorithm should be computed using the relation e(i,j)=[(Xi)^(2-m)]*Omega(1/Xi)/Lambda'(1/Xi) 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, Vikram

Reply by ●February 14, 20052005-02-14

"Jaco Versfeld" <jaco_versfeld@hotmail.com> asked in message news:e48813da.0502102140.21ec1f3a@posting.google.com...> 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])?See Equation (7) in http://www.ifp.uiuc.edu/~sarwate/decoder.ps

Reply by ●February 15, 20052005-02-15