```>On 9 mar, 04:08, "nezhate" <mazouz.nezh...@gmail.com> wrote:
>> Hi all,
>> What does the reed solomon decoder outputs in the case when we have
>> more than "t" errors to correct?
>> Does he correct some errors and leave other errors as they came, or he
>> will correct any thing (i.e the data that was in the input will appear
>> in the output)?
>
>If you have more than "t" errors, the decoder cannot correct
>anything...
>So you have to detect this failure to bypass the decoder... by
>comparing the number of zero in the locator and the degree of the
>locator polynomial from the berlekamp algorithm
>
>

So, let me see if I have understood this:  if the number of errors is
greater than "t", the decoder doesn't work at all, am I right?
My question is: is there any way of preventing this? or at least try to
correct it?
Thanks,
```
```On Mar 9, 3:40 pm, "dvsarw...@gmail.com" <dvsarw...@gmail.com> wrote:
> On Mar 9, 7:56 am, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
> wrote:
>
> > If there is more errors then it can be corrected by the code, the
> > attempt to correct it only makes the things worse. The good decoder
> > should detect this situation.
>
> One other possibility is that the decoder output is the *wrong*
> codeword because the received word is at distance t or less
> from the wrong codeword and at distance more than t from
> the transmitted codeword.  This is a *valid* decoding in that
> the decoder has found the codeword that is at distance t or
> less from the received word, and that is exactly what the decoder
> is designed to do!  Of course, the output is incorrect because
> the codeword produced is not the one that was transmitted: too
> many errors have occurred in the channel.  This event -- that
> the decoder output is a valid codeword but *not* the transmitted
> codeword -- is quite rare: its probability is generally much smaller
> than the probability that the decoder is unable to  correct the
> errors (because more than t errors have occurred) and indicates
> this failure to the destination of the data, or requests a repeat
> transmission from the data source.
>
> --Dilip Sarwate

Hi again!
I implemented on FPGA RS decoder using your paper (Berlekamp-massey
algorithm). when there is t errors or less, all works and the decoder
when I have more than t errors, the decoder (of courses!) can't
correct the received code and it outputs the received code as it is.
Should I consider that in this case my decoder is well working? Does
this agrees with the
theoretical part?
Thanks.

```
```
Eric Jacobsen wrote:

>>>If there is more errors then it can be corrected by the code, the
>>>attempt to correct it only makes the things worse.

[...]

>> This event -- that
>> the decoder output is a valid codeword but *not* the transmitted
>>codeword -- is quite rare: its probability is generally much smaller
>>than the probability that the decoder is unable to  correct the
>>errors

[...]

> This definitely happens in real systems.   We tried to use the decoder
> output error syndrome to measure codeword error rate on one system,
> but the SNR region between which there were no errors and where the
> codewords started aliasing was too narrow to be useful for our
> purposes at the time.

Agreed completely. For the good codes, there is not much of no man's
land between the spheres of the radius t. Hence the code should not be
used to the full error correction capacity, and/or there should be some
other means to ensure the integrity of the data.

> If the input error rate is too high the decoder may have no way to
> know that it's not decoding incorrectly if it can find a valid
> codeword within acceptable distance to what was received.

For the normal operation, the input BER should be at least several times
less then the maximum correcting capacity of the code.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com
```
```On 9 Mar 2007 06:40:14 -0800, "dvsarwate@gmail.com"
<dvsarwate@gmail.com> wrote:

>On Mar 9, 7:56 am, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
>wrote:
>
>> If there is more errors then it can be corrected by the code, the
>> attempt to correct it only makes the things worse. The good decoder
>> should detect this situation.
>
>
>One other possibility is that the decoder output is the *wrong*
>codeword because the received word is at distance t or less
>from the wrong codeword and at distance more than t from
>the transmitted codeword.  This is a *valid* decoding in that
>the decoder has found the codeword that is at distance t or
>less from the received word, and that is exactly what the decoder
>is designed to do!  Of course, the output is incorrect because
>the codeword produced is not the one that was transmitted: too
>many errors have occurred in the channel.  This event -- that
>the decoder output is a valid codeword but *not* the transmitted
>codeword -- is quite rare: its probability is generally much smaller
>than the probability that the decoder is unable to  correct the
>errors (because more than t errors have occurred) and indicates
>this failure to the destination of the data, or requests a repeat
>transmission from the data source.
>
>--Dilip Sarwate

Dilip beat me to it.

This definitely happens in real systems.   We tried to use the decoder
output error syndrome to measure codeword error rate on one system,
but the SNR region between which there were no errors and where the
codewords started aliasing was too narrow to be useful for our
purposes at the time.

If the input error rate is too high the decoder may have no way to
know that it's not decoding incorrectly if it can find a valid
codeword within acceptable distance to what was received.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org
```
```On Mar 9, 7:56 am, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
wrote:

> If there is more errors then it can be corrected by the code, the
> attempt to correct it only makes the things worse. The good decoder
> should detect this situation.

One other possibility is that the decoder output is the *wrong*
codeword because the received word is at distance t or less
from the wrong codeword and at distance more than t from
the transmitted codeword.  This is a *valid* decoding in that
the decoder has found the codeword that is at distance t or
less from the received word, and that is exactly what the decoder
is designed to do!  Of course, the output is incorrect because
the codeword produced is not the one that was transmitted: too
many errors have occurred in the channel.  This event -- that
the decoder output is a valid codeword but *not* the transmitted
codeword -- is quite rare: its probability is generally much smaller
than the probability that the decoder is unable to  correct the
errors (because more than t errors have occurred) and indicates
this failure to the destination of the data, or requests a repeat
transmission from the data source.

--Dilip Sarwate

```
```
nezhate wrote:

> Hi all,
> What does the reed solomon decoder outputs in the case when we have
> more than "t" errors to correct?
> Does he correct some errors and leave other errors as they came, or he
> will correct any thing (i.e the data that was in the input will appear
> in the output)?

If there is more errors then it can be corrected by the code, the
attempt to correct it only makes the things worse. The good decoder
should detect this situation.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com
```
```On 9 mar, 04:08, "nezhate" <mazouz.nezh...@gmail.com> wrote:
> Hi all,
> What does the reed solomon decoder outputs in the case when we have
> more than "t" errors to correct?
> Does he correct some errors and leave other errors as they came, or he
> will correct any thing (i.e the data that was in the input will appear
> in the output)?

If you have more than "t" errors, the decoder cannot correct
anything...
So you have to detect this failure to bypass the decoder... by
comparing the number of zero in the locator and the degree of the
locator polynomial from the berlekamp algorithm

```
```Hi all,