# Order of encoder output in Reed-Solomon encoding

Started by March 8, 2005
```Hello:
I had a query regarding the encoder transmission format order at the
Reed-Solomon encoder output for the commercial standards such as
European DVB, North American ATSC/ITU-J83 standards etc.

For a RS (n,k) code, if the message polynomial is :
m(x)=m(0)+m(1)*x+m(2)*x^2+......+m(k-1)*x^(k-1)
and the parity polynomial is :
c(x)=c(0)+c(1)*x+...........+c(n-k-1)*x^(n-k-1).

Is the reed-solomon encoder format output by these standards given as:

r=[m(0) m(1) .....m(k-1) c(0) c(1) .....c(n-k-1)]

or

r=[m(k-1) m(k-2) ......m(0) c(n-k-1) ....c(1) c(0)] ????

This is very important since the decoder needs to be aware of the
format of the transmission at the encoder side..

Any help would be greatly appreciated.

Vikram

```
```>Hello:
>I had a query regarding the encoder transmission format order at the
>Reed-Solomon encoder output for the commercial standards such as
>European DVB, North American ATSC/ITU-J83 standards etc.
>
>For a RS (n,k) code, if the message polynomial is :
>m(x)=m(0)+m(1)*x+m(2)*x^2+......+m(k-1)*x^(k-1)
>and the parity polynomial is :
>c(x)=c(0)+c(1)*x+...........+c(n-k-1)*x^(n-k-1).
>
>Is the reed-solomon encoder format output by these standards given as:
>
>r=[m(0) m(1) .....m(k-1) c(0) c(1) .....c(n-k-1)]
>
>or
>
>r=[m(k-1) m(k-2) ......m(0) c(n-k-1) ....c(1) c(0)] ????
>
>This is very important since the decoder needs to be aware of the
>format of the transmission at the encoder side..
>
>Any help would be greatly appreciated.
>
>Vikram
>
>

Hi Vikram,

Co-efficient of highest order X is the first to ENTER the encoder, first
to LEAVE the encoder. It is also the FIRST to enter the decoder and exit
the decoder... !

Rider

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```