Reed Solomon vs Convolutional coding

I have several doubts about this coded forms.

It is known that Reed-Solomon is a good code agains burns errors. 

Also, it is known that Concatenated Reed-Solomon and convolutional coding
with interlaving run very cool.

But i want compare only a simple Reed-Solomon versus a Convolutional
coding with a good interleaving. 

I think that if you put an interleaver-deinterlaver system, then you
should not have problems with burns error if you use convolutional coding.
Then, in this sense, i would like to know which is better. ¿?

We can consider as Reed-Solomon a RS(255,223) (u other), and as
convolutional coding we consider the popular 1/2 K=7 NASA standard.

¿somebody has graphicals of Eb/N0 vs Pb?

JAlbertoDJ wrote:
> I have several doubts about this coded forms.
> 
> It is known that Reed-Solomon is a good code agains burns errors. 
> 
> Also, it is known that Concatenated Reed-Solomon and convolutional coding
> with interlaving run very cool.
> 
> But i want compare only a simple Reed-Solomon versus a Convolutional
> coding with a good interleaving. 
> 
> I think that if you put an interleaver-deinterlaver system, then you
> should not have problems with burns error if you use convolutional coding.
> Then, in this sense, i would like to know which is better. ¿?
> 
> We can consider as Reed-Solomon a RS(255,223) (u other), and as
> convolutional coding we consider the popular 1/2 K=7 NASA standard.
> 
> ¿somebody has graphicals of Eb/N0 vs Pb?

Any good text book on channel coding, e.g., Lin/Costello - Error Control 
Coding.

Laurent

>I have several doubts about this coded forms.
>
>It is known that Reed-Solomon is a good code agains burns errors. 
>
>Also, it is known that Concatenated Reed-Solomon and convolutional
coding
>with interlaving run very cool.
>
>But i want compare only a simple Reed-Solomon versus a Convolutional
>coding with a good interleaving. 
>
>I think that if you put an interleaver-deinterlaver system, then you
>should not have problems with burns error if you use convolutional
coding.
>Then, in this sense, i would like to know which is better. ¿?
>
>We can consider as Reed-Solomon a RS(255,223) (u other), and as
>convolutional coding we consider the popular 1/2 K=7 NASA standard.
>
>¿somebody has graphicals of Eb/N0 vs Pb?
>

I had asked the same que few months back I guess. Search this forum.

However, I wanted to compare like-wise-like.

What you are doing is not fair. Your RS code is not rate 1/2 whereas ur
Conv code is rate 1/2.

In terms of your ans: Rate 1/2 conv code with K=7 will perform better than
rate 1/2 RS code of (255,127) on AWGN channel. This is what I think.

On different channel conditions and SNRs, it depends on other factors.

Hope this helps.

Chintan

There is one interesting theoretical point embedded in this
question, which is that if you deal with burst errors by
interleaving them so that they appear random, you are
discarding information and, therefore, approaching the
coding problem suboptimally.

This may not tilt things solidly towards Reed-Solmon codes,
depending upon all the other usual factors; but it's
something to consider.

Steve

>There is one interesting theoretical point embedded in this
>question, which is that if you deal with burst errors by
>interleaving them so that they appear random, you are
>discarding information and, therefore, approaching the
>coding problem suboptimally.
>
>This may not tilt things solidly towards Reed-Solmon codes,
>depending upon all the other usual factors; but it's
>something to consider.
>
>Steve
>

Could you explain better about "discardind information". What i say is, in
transmission, interleave the order of symbols after convolutional encoder.

Then in reception, first de-interleaver the symbols and after run Viterbi
decode. Explain why this method is suboptimal, please.

Steve Pope wrote:

> There is one interesting theoretical point embedded in this
> question, which is that if you deal with burst errors by
> interleaving them so that they appear random, you are
> discarding information and, therefore, approaching the
> coding problem suboptimally.

If we know the distribution of errors, we can design a code which makes 
use of that distribution. Interleaving is crude way to do that.

Going the other way, i.e. designing a decoding algorithm for a given 
code so it would be optimal for the particular error distibution, seems 
to be more difficult problem.

> This may not tilt things solidly towards Reed-Solmon codes,
> depending upon all the other usual factors; but it's
> something to consider.

GF(2^n) codes are unoptimal for the purpose of burst correction either: 
if errors appear in packs, it doesn't mean all bits in the pack are corrupt.

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

>
>I had asked the same que few months back I guess. Search this forum.
>
>However, I wanted to compare like-wise-like.
>
>What you are doing is not fair. Your RS code is not rate 1/2 whereas ur
>Conv code is rate 1/2.
>
>In terms of your ans: Rate 1/2 conv code with K=7 will perform better
than
>rate 1/2 RS code of (255,127) on AWGN channel. This is what I think.
>
>On different channel conditions and SNRs, it depends on other factors.
>
>Hope this helps.
>
>Chintan
>

It is true, then we have to consider an RS(31,15) versus k=7 1/2, for
example. Also, in this comparative, BW occuppied would not be a problem. 

The question is that yesterday, i read something about Voyager missions.
It result that with a Pe=0.005 there is not differrent (only 0.2 dBs)
between Viterbi k=7 1/2 or a RS(255,223) concatenated with the same Viterbi
k=7 1/2. Only for low probabilities of bit error the concatenated system is
better than no-concatenated system. For example, for not compressed images,
Voyager did not use concatenated code. Otherwise, for compressed image PB
requeriments were others: Pb=1*10e-5. Then in this case Voyager transmitted
with the concatenated system.

In my case, a poor Pb=0.01 is enough for my system. So, i am looking for a
channel code optimum for that Pb. Now i know than RS concatenated with
Viterbi not run well in thats situationb, and i suppose that a simple RS
code neither.

Also, i am reading something about Turbo-codes, but this is only better
than convolutional code for long blocks of bit. With short lenght a
turbo-code is worst than simple convolutional code.

¿?

JAlbertoDJ wrote:


> In my case, a poor Pb=0.01 is enough for my system. So, i am looking for a
> channel code optimum for that Pb.

If the target bit error rate is as high as 0.01, you are not going to 
gain much by using any reasonable coding. You'd be better by using the 
direct uncoded modulation, especially if you account for the modem losses.


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

Vladimir Vassilevsky  <nospam@nowhere.com> wrote:

>Steve Pope wrote:

>> There is one interesting theoretical point embedded in this
>> question, which is that if you deal with burst errors by
>> interleaving them so that they appear random, you are
>> discarding information and, therefore, approaching the
>> coding problem suboptimally.

>If we know the distribution of errors, we can design a code which makes 
>use of that distribution. 

Correct

>Interleaving is crude way to do that.

I'm not sure it accomplishes this at all; if after interleaving
the errors are in random location, then we have lost information.

However it could be argued that after interleaving, the errors
are separated by a more-than-random amount, and the target 
convultional code takes advantage of this.  I've never been
quite convinced it works out that way.

>Going the other way, i.e. designing a decoding algorithm for a given 
>code so it would be optimal for the particular error distibution, seems 
>to be more difficult problem.

It's often easy to show that on a random-error channel, the
convolutional code is closer to capacity; whereas on a channel
exhibiting (for example) mostly 2-bit burst errors, the
RS code outperforms the convolutional.

What's difficult is computing capacity (and as you state, optimal
coding) for these non-random channels.

Steve

>Vladimir Vassilevsky  <nospam@nowhere.com> wrote:
>
>>Steve Pope wrote:
>
>>> There is one interesting theoretical point embedded in this
>>> question, which is that if you deal with burst errors by
>>> interleaving them so that they appear random, you are
>>> discarding information and, therefore, approaching the
>>> coding problem suboptimally.
>
>>If we know the distribution of errors, we can design a code which makes

>>use of that distribution. 
>
>Correct
>
>>Interleaving is crude way to do that.
>
>I'm not sure it accomplishes this at all; if after interleaving
>the errors are in random location, then we have lost information.
>
>However it could be argued that after interleaving, the errors
>are separated by a more-than-random amount, and the target 
>convultional code takes advantage of this.  I've never been
>quite convinced it works out that way.
>
>>Going the other way, i.e. designing a decoding algorithm for a given 
>>code so it would be optimal for the particular error distibution, seems

>>to be more difficult problem.
>
>It's often easy to show that on a random-error channel, the
>convolutional code is closer to capacity; whereas on a channel
>exhibiting (for example) mostly 2-bit burst errors, the
>RS code outperforms the convolutional.
>
>What's difficult is computing capacity (and as you state, optimal
>coding) for these non-random channels.
>
>Steve
>
%%%

Hi 

Sorry to say this but can you please explain why with interleaving the
information is lost.?

What I understand is that with iterative decoding and all that stuff we
can achieve pretty low bit error rates.

So where do we loose the information?

Thanks

Chintan