# Reed solomon with erasures

Started by July 11, 2008
```Hello,

I'm interested in using RS- Reed solomon codes with erasures.

I know the RS code can correct 2g+e=n-k, where g is erasure and e is
error.

My system can find the erasures with high probability.
My question is, if the system can detect X erasures but 50% of them are
correct.
Meaning they were mistakenly detected as erasures.
Will I earn something using decoder with erasure or using regular decoding
?

Another question, if from the X erasures 75% are correct.
Will I earn something ?

thanks

Itzic

```
```On Jul 11, 11:53 am, "shimi" <itzic...@yahoo.com> wrote:
> Hello,
>
> I'm interested in using RS- Reed solomon codes with erasures.
>
> I know the RS code can correct 2g+e=n-k, where g is erasure and e is
> error.
>
> My system can find the erasures with high probability.
> My question is, if the system can detect X erasures but 50% of them are
> correct.
> Meaning they were mistakenly detected as erasures.
> Will I earn something using decoder with erasure or using regular decoding
> ?
>
> Another question, if from the X erasures 75% are correct.
> Will I earn something ?
>
> thanks
>
> Itzic

Probably depends upon the error rate of the mistakenly-classified
bits. If all of the bits that your receiver incorrectly marks as
erasures are correct, then you would be best served to include them.
If the error rate is high for those bit positions, then you're best
off just marking them as erasures. Other error rates give you a case

Jason
```
```
shimi wrote:
> Hello,
>
> I'm interested in using RS- Reed solomon codes with erasures.
>
> I know the RS code can correct 2g+e=n-k, where g is erasure and e is
> error.
>
> My system can find the erasures with high probability.
> My question is, if the system can detect X erasures but 50% of them are
> correct.
> Meaning they were mistakenly detected as erasures.
> Will I earn something using decoder with erasure or using regular decoding
> ?
>
> Another question, if from the X erasures 75% are correct.
> Will I earn something ?

In general, any apriori knowledge about the errors improves the
operation of the decoder. There is a family of algorithms of different
complexity for decoding of the RS codes with the use of the reliability
information for every symbol. Depending on the algorithm and the error
rate, you can expect the gain of 0.5 to 3dB compared to the hard
decision algebraic decoding.

DSP and Mixed Signal Design Consultant
http://www.abvolt.com

```
```On 2008-07-11, shimi <itzic100@yahoo.com> wrote:
> I'm interested in using RS- Reed solomon codes with erasures.
>
> I know the RS code can correct 2g+e=n-k, where g is erasure and e is
> error.

Actually it's 2e+g=n-k.  You can correct more erasures than errors.
Think about it this way:  The error correcting power can be applied to
both *finding* and *fixing* (the error case) or just *fixing* if you
supply the location information using outside information.

> My system can find the erasures with high probability.

You will always gain from that.

--
<ben@ben.com>
http://www.ben.com/
```
```Hi All

Which is better: Reed Solomon coding or convolutional code with SOVA
decoding?

Thanks

Regards,

Chintan
```
```On 2008-07-11, cpshah99 <cpshah99@rediffmail.com> wrote:
>
> Which is better: Reed Solomon coding or convolutional code with SOVA
> decoding?

It will depend on all kinds of things.  For a primer try the telecom
part of NASA's "basics of space flight":

http://www2.jpl.nasa.gov/basics/bsf10-1.html

--
<ben@ben.com>
http://www.ben.com/
```
```
cpshah99 wrote:

> Which is better: Reed Solomon coding or convolutional code with SOVA
> decoding?

It depends. BTW, Reed Solomon codes can be decoded with SOVA as well.