I am normally a speech/audio processing engineer, so this is somewhat out
of my primary expertise area.
I have recently implemented the Reed Solomon error correction algorithm
and have gotten it to work for the following case: the roots of the
generator polynomial are in positions 1 through 2t, where t is the number
of errors. However, I implemented the case where the roots of the
generator polynomial start at n, where n > 1. I looked through many
library books and found a formula for finding the error values in only a
couple of books. The problem is that it does not work. I found errors in
several books concerning Reed Solomon, and there are a lot of details not
explained in most texts.
I am looking for reliable and accurate equations for finding the error
values when the generator polynomial roots start in a position greater
than
1.
When I implemented the case where the generator polynomial roots start in
position 1, you have the omega polynomial in the numerator and the
derivative of the sigma polynomial in the denominator. The coefficient
becomes 1. This works fine.
The forumla for the case of n > 1, is the same except the coefficient is
given as:
- alpha^(j(1-n))
where n is the index for the first root of the generator polynomial.
This doesn't work, as I am stress testing the algorithm over thousands of
randomly generated messages.
Thank you for any information, either formulas or books and articles or
code that clearly explain this.
I also have another question: we were asked to implement am (n,k) code,
but the particular values of n and K are not listed in any table of valid
BCH codes. The textbooks, however, refer to R-S as a type of BCH code.
Does this mean that R-S cannot work with these values of n and h? I have
a
specification in front of me with these values of n and k, and also the
AHA
website seems to have an implementation of it running online (without the
equations or source available). Is it possible to have an R-S decoder for
values of (n,k) that are not listed in the tables of BCH codes?
Linda Seltzer
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