# A Reed-Solomon Decoder Question

Started by June 16, 2009
```Hi Guys,
I am hoping someone in this group would be able to answer this
question. I am working on a Reed-Solomon decoder for WiMAX
802.16-2004. Its a RS(255,239,T=8) code.
The generator polynomial is  g(x) = (x + a^0)(x + a^1)(x + a^2) ...(x
+ a^(2T-1))
You'll notice that the first root of g(x) is 1.

I have run into a problem when I use this g(x). It seems the error
evaluator polynomial is not being calculated corectly  by my modified
euclidean algorithm but the error locator polynomial being calculated
is correct.

If I use a generator polynomial which has a^1 as its first root i.e g
(x) = (x + a^1)(x + a^2) ...(x + a^2T)
then both polynomials are being correctly calculated by the Euclids
algorithm. I haven't been able to find any info on what needs to be
tweaked if the first root is not a^1.

I hope some has a solution for this.

Thanks
Sudhir
```
```On Jun 16, 5:58&#2013266080;pm, Sudhir Singh <Sudhir.Si...@email.com> wrote:

> I haven't been able to find any info on what needs to be
> tweaked if the first root is not a^1.

Assuming that you have programmed the Euclidean
algorithm correctly, your program will give you the
error-evaluator polynomial, but the answer that you
will get when the first root is a^1 is not the same as
the answer you will get when the first root is a^0 = 1.
Note:  the Euclidean algorithm does not know
(and does not need to know) whether the first root of
g(x) is a^0 or a^1 or whatever: it returns the correct
error-evaluator polynomial, but how you use it
thereafter can cause you much grief.

The definition of the error-evaluator polynomial depends
on what the first root is, and correspondingly, the Forney
error value formula also depends on what the first root
is.  So if your first root is a^0, use the corresponding
Forney formula and you will get the error values that you
know that you are supposed to get.  But if instead you
use the Forney formula for the case of first root being
a^1 with the error evaluator polynomial for the case of
first root being a^0, you will not get the error values, and
you may suspect that something is wrong with the
Euclidean algorithm.

See the paper at
(http://www.ifp.illinois.edu/~sarwate/pubs/Sarwate01High.pdf)
for the definitions of the various polynomials, the Forney
formula, etc. for the case when the first root is not a^1.
The paper itself deals with Berlekamp-Massey decoders,
but the basic stuff is all the same.

Hope this helps.

--Dilip Sarwate
```
```Hi Dilip

Thanks a lot for your help. I have got my decoder working now.

Cheers
Sudhir

```