Reed Solomon Simulation

On Sun, 26 Oct 2008 08:05:48 -0700 (PDT), "dvsarwate@yahoo.com"
<dvsarwate@gmail.com> wrote:

>On Oct 24, 6:32&#4294967295;pm, Eric Jacobsen <eric.jacob...@ieee.org> wrote:
>
>>
>> The relative complexities (of the encoders and decoders) are an
>> important metric to consider as well. &#4294967295; Running an RS encoder or
>> decoder at such a low rate is usually inefficient compared to a decent
>> Viterbi decoder. &#4294967295; The RS encoder will always be far more complex than
>> the CC encoder, especially at R=1/2.
>>
>
>True.  But an RS encoder/decoder for a (32,16) RS code over
>GF(256) obtained by shortening a (255,239) RS code has the
>same complexity as the original code.

Yes, and since the larger codeword has to be processed far more
frequently (every 32 bytes received rather than every 255 or 204 or
whatever) there may need to be parallel instantiations needed in order
to keep up.   That's just comparing to the typical 255 or 204-byte
codewords.

>  On the other hand,
>a (256,128) RS code or (255,127) RS code would be totally
>impractical.

Agreed.   I suspect that's why we don't see them used in practice.  ;)

>A (32,16) RS code over GF(256) s a very powerful code but
>with *many* weak spots for use on an AWGN channel where
>it would typically be implemented as a (256,128) binary code
>with antipodal PSK signaling.  This code is guaranteed to
>correct all (single) bursts of errors as long as 50 bits of the 256
>bits in a block, and *some* bursts of longer lengths (up to 64
>bits) can also be corrected.  But there are random bit errors
>of as few as 9 bits that the code is unable to correct.
>Unfortunately,
>on an AWGN channel, random bit errors are generally more
>likely to occur than long bursts.  A better modulation scheme for
>an RS code on an AWGN channel would be M-ary orthogonal
>FSK, but nobody wants to use that, do they?
>
>--Dilip Sarwate

Not if M is very large at all.

Agreed on your points, as usual.   Depending on what the OP is doing
I'm interested in his results.   There are cases in industry where
RS-only FEC is used in practice, usually with reasonably high order
modulation and the typical high code rates.   I've not seen such a
low-rate used before, though.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php

dvsarwate@yahoo.com <dvsarwate@gmail.com> wrote:

>But an RS encoder/decoder for a (32,16) RS code over
>GF(256) obtained by shortening a (255,239) RS code has the
>same complexity as the original code.  

Slight nitpick: on a per-decoded bit basis, it has higher
complexity.  On a per-codeword basis, it has about the
same complexity, but the codewords have fewer bits.

>A (32,16) RS code over GF(256) s a very powerful code but
>with *many* weak spots for use on an AWGN channel where
>it would typically be implemented as a (256,128) binary code
>with antipodal PSK signaling.  This code is guaranteed to
>correct all (single) bursts of errors as long as 50 bits of the 256
>bits in a block, and *some* bursts of longer lengths (up to 64
>bits) can also be corrected.  But there are random bit errors
>of as few as 9 bits that the code is unable to correct.

On an AWGN channel, if you are using a RS code with a given
code rate and a given number of bits per codeword, you are
best off using the smallest possible field size.  Thus,
this rate 1/2 code has 256 bits per codeword; a 6-bit
(42,21) RS code has roughly the same number of bits per codeword
but performs better.  (And, a binary BCH code performs better
still, if the channel is truly AWGN without bursts.)

An interesting possibility for larger codeword sizes is
to use an algebraic geometry code.

Steve

Hello 

I have completed the simulation of rate 1/2 RS code as Dr. Sarwate
suggested. Now, the way I have done is as follows, the channel is AWGN and
BPSK modulation:

data=randint(1,16,256);
data_pad=[zeros(1,223) data];
code=rsenc(data_pad,255,239);
actual_code=code(224:end); which gives me 32 symbols.

and exactly opp at receiver. This works fine and if I remove noise I am
getting 0 BER.

But the way I am scaling the noise is:

sigma=sqrt(1/(2*R_c*snr_lin));

where R_c=239/255. By doing this way, at 4.5 dB, I am getting BER of
9e-5;

Ideally, R_c=1/2, but if I use R_c=0.5, at 4.5 dB I am geting BER of
1e-2.

Is this correct?

Chintan

On Oct 26, 11:24&#4294967295;pm, "cpshah99" <cpsha...@rediffmail.com> wrote:

> the channel is AWGN and BPSK modulation:
>
> data=randint(1,16,256);
> data_pad=[zeros(1,223) data];
> code=rsenc(data_pad,255,239);
> actual_code=code(224:end); which gives me 32 symbols.

> But the way I am scaling the noise is:
>
> sigma=sqrt(1/(2*R_c*snr_lin));
>
> where R_c=239/255. By doing this way, at 4.5 dB, I am getting BER of
> 9e-5;
>
> Ideally, R_c=1/2, but if I use R_c=0.5, at 4.5 dB I am geting BER of
> 1e-2.


Chintan:

You ask, Is this correct?

Well, it depends on whether you want to get the right
answer or the answer that you *want* to get, viz., your
RS code will perform better than a rate 1/2 convolutional
code.  The code that you are using is a rate 1/2 code,
and so you should use R_c = 1/2, and not R_c = 239/255,
shouldn't you?

Uncoded PSK on an AWGN channel has BER just a little
below 10^-2 at 4.5 dB.  If a rate 1/2 code is used, the
raw channel bit error rate is much higher, about 0.046 or
so, and thus an 8-bit RS symbol has a high probability
of being incorrect, likely enough to overwhelm the error
correcting capability of the code.  It is not surprising that
your simulation gives a rather large decoded BER
(assuming that it has been done correctly).  Making the
answer more palatable (to yourself) by using the wrong
code rate and hence the wrong SNR is not the way to go.
It will make the denizens of comp.dsp very suspicious of
any results that you report in the future.

Dilip Sarwate

Hi Sir!

I really want the *right* answer not the answer *I want*.

Even I had some doubts regarding my simulation, so what I did is that I
used RS code of (255,127) which is definately rate 1/2 code.

So, now I am getting BER of 1e-4 at 5.5 dB.

I *think* this correct, I might be wrong. 

I would really appreciate your opinion. I dont want to report any wrong
results.

Regards,

Chintan