Vladimir Vassilevsky <antispam_bogus@hotmail.com> wrote:
>Assume the disastrous Eb/No with the huge amount of random errors.
>Then the probability of the undetected error for RS code with K
>redundancy symbols in GF(M):
>p = {sum C(M-1,x)}/M^K
> x <= K/2
I would say this formula is missing N, the total number
of symbols in a codeword. I would replace the "M-1" with N.
I also think you need another factor of (M-1)^x within
the summation.
Steve
Reply by Vladimir Vassilevsky●November 8, 20082008-11-08
Steve Pope wrote:
> Vladimir Vassilevsky <antispam_bogus@hotmail.com> wrote:
>
>
>>Raymond Toy wrote:
>
>
>>>Yes, I understand the RS code could produce no error indication, and
>>>the CRC could detect that.
>>>But the CRC takes extra bits, so if I added an extra parity word or
>>>two to the RS code, would I get better or worse performance than with
>>>the CRC?
>
>
>>This is a system question.
>
>
> Actually, it sounds like more of a mathematics question to me.
> Rephrased, does a given number number of bits of CRC give
> you better, worse, or about the same error-detection as the same
> number of added bits of RS redundancy?
>
> Some would argue that the added RS redundancy is better, based
> on a minimum weight argument.
Assume the disastrous Eb/No with the huge amount of random errors.
Then the probability of the undetected error for RS code with K
redundancy symbols in GF(M):
p = {sum C(M-1,x)}/M^K
x <= K/2
You have to run the numbers to compare this to 1/2^N for CRC.
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com
Reply by Eric Jacobsen●November 7, 20082008-11-07
On Sat, 8 Nov 2008 01:27:07 +0000 (UTC), spope33@speedymail.org (Steve
Pope) wrote:
>Vladimir Vassilevsky <antispam_bogus@hotmail.com> wrote:
>
>>Raymond Toy wrote:
>
>>> Yes, I understand the RS code could produce no error indication, and
>>> the CRC could detect that.
>>> But the CRC takes extra bits, so if I added an extra parity word or
>>> two to the RS code, would I get better or worse performance than with
>>> the CRC?
>
>>This is a system question.
>
>Actually, it sounds like more of a mathematics question to me.
>Rephrased, does a given number number of bits of CRC give
>you better, worse, or about the same error-detection as the same
>number of added bits of RS redundancy?
>
>Some would argue that the added RS redundancy is better, based
>on a minimum weight argument.
>
>Steve
Could be, but in a system you can protect/cover multiple codewords
with a single CRC, so I think part of the answer may depend on the
nature of the transmissions. If the transmissions are long enough, a
single CRC could protect a number of codewords and add relatively
little overhead.
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org
Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
Reply by Steve Pope●November 7, 20082008-11-07
Vladimir Vassilevsky <antispam_bogus@hotmail.com> wrote:
>Raymond Toy wrote:
>> Yes, I understand the RS code could produce no error indication, and
>> the CRC could detect that.
>> But the CRC takes extra bits, so if I added an extra parity word or
>> two to the RS code, would I get better or worse performance than with
>> the CRC?
>This is a system question.
Actually, it sounds like more of a mathematics question to me.
Rephrased, does a given number number of bits of CRC give
you better, worse, or about the same error-detection as the same
number of added bits of RS redundancy?
Some would argue that the added RS redundancy is better, based
on a minimum weight argument.
Steve
Reply by Vladimir Vassilevsky●November 7, 20082008-11-07
Raymond Toy wrote:
> Yes, I understand the RS code could produce no error indication, and
> the CRC could detect that.
> But the CRC takes extra bits, so if I added an extra parity word or
> two to the RS code, would I get better or worse performance than with
> the CRC?
This is a system question. What is the cost of an undetected random
error in the data vs the cost of the whole data been rejected because of
uncorrectable errors?
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com
Reply by Raymond Toy●November 7, 20082008-11-07
>>>>> "Eric" == Eric Jacobsen <eric.jacobsen@ieee.org> writes:
Eric> On Fri, 07 Nov 2008 14:15:51 -0500, Jerry Avins <jya@ieee.org> wrote:
>> Raymond Toy wrote:
>>> But doesn't the RS code already have pretty good detection
>>> capabilities? Would adding a CRC really improve things more than,
>>> say, adding another RS parity word or two?
>>
>> When the decoding produces no error indication but is nevertheless wrong.
>>
>> Jerry
Eric> Exactly. When there are too many errors the RS can (and often will)
Eric> pick a valid codeword that is not the codeword that was transmitted.
Eric> With a valid, but incorrect, codeword selected it will not indicate
Eric> any error syndrome and the only way to know for certain whether the
Eric> data is correct is with some other detection method, like a CRC.
Yes, I understand the RS code could produce no error indication, and
the CRC could detect that. (I guess that's particularly good since
CRCs are good at detecting burst errors and the RS failure will
produce burst errors.)
But the CRC takes extra bits, so if I added an extra parity word or
two to the RS code, would I get better or worse performance than with
the CRC?
Ray
Reply by Eric Jacobsen●November 7, 20082008-11-07
On Fri, 07 Nov 2008 14:15:51 -0500, Jerry Avins <jya@ieee.org> wrote:
>Raymond Toy wrote:
>>>>>>> "Vladimir" == Vladimir Vassilevsky <antispam_bogus@hotmail.com> writes:
>>
>> Vladimir> marval wrote:
>>
>> >> Hi:
>> >> I am a newbie on Reed-Solomon coding, and I was wondering what
>> >> happens
>> >> when the received message has more errors than the error correcting
>> >> capacity 2t.
>>
>> Vladimir> For the hard decision, the corrupt codeword can either fall on the no
>> Vladimir> man land, so you know that it can't be corrected; or it will be
>> Vladimir> aliased to the adjacent codeword and mistakenly decoded. For the soft
>> Vladimir> decision, the corrupt codeword will be decoded to the most likely
>> Vladimir> codeword which is going to be wrong.
>>
>> Vladimir> I would say that the decoding fails completely, but I am not
>> >> sure. Could anybody explain this to me?, is there anyway to prevent
>> >> my decoding
>> >> from crashing when the received message contains more than 2t errors?
>>
>> Vladimir> The standard practice is adding some integrity check for data, like
>> Vladimir> CRC, for example. So you know that the decoding process failed.
>>
>> But doesn't the RS code already have pretty good detection
>> capabilities? Would adding a CRC really improve things more than,
>> say, adding another RS parity word or two?
>
>When the decoding produces no error indication but is nevertheless wrong.
>
>Jerry
Exactly. When there are too many errors the RS can (and often will)
pick a valid codeword that is not the codeword that was transmitted.
With a valid, but incorrect, codeword selected it will not indicate
any error syndrome and the only way to know for certain whether the
data is correct is with some other detection method, like a CRC.
If the system only ever operates in a region where codeword aliasing
never happens, then this isn't needed. The error curves for RS
systems are quite steep, though, so often the difference between being
error-free and having aliased codewords is only a dB or two.
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org
Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
Reply by Jerry Avins●November 7, 20082008-11-07
Raymond Toy wrote:
>>>>>> "Vladimir" == Vladimir Vassilevsky <antispam_bogus@hotmail.com> writes:
>
> Vladimir> marval wrote:
>
> >> Hi:
> >> I am a newbie on Reed-Solomon coding, and I was wondering what
> >> happens
> >> when the received message has more errors than the error correcting
> >> capacity 2t.
>
> Vladimir> For the hard decision, the corrupt codeword can either fall on the no
> Vladimir> man land, so you know that it can't be corrected; or it will be
> Vladimir> aliased to the adjacent codeword and mistakenly decoded. For the soft
> Vladimir> decision, the corrupt codeword will be decoded to the most likely
> Vladimir> codeword which is going to be wrong.
>
> Vladimir> I would say that the decoding fails completely, but I am not
> >> sure. Could anybody explain this to me?, is there anyway to prevent
> >> my decoding
> >> from crashing when the received message contains more than 2t errors?
>
> Vladimir> The standard practice is adding some integrity check for data, like
> Vladimir> CRC, for example. So you know that the decoding process failed.
>
> But doesn't the RS code already have pretty good detection
> capabilities? Would adding a CRC really improve things more than,
> say, adding another RS parity word or two?
When the decoding produces no error indication but is nevertheless wrong.
Jerry
--
Engineering is the art of making what you want from things you can get.
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Reply by Raymond Toy●November 7, 20082008-11-07
>>>>> "Vladimir" == Vladimir Vassilevsky <antispam_bogus@hotmail.com> writes:
Vladimir> marval wrote:
>> Hi:
>> I am a newbie on Reed-Solomon coding, and I was wondering what
>> happens
>> when the received message has more errors than the error correcting
>> capacity 2t.
Vladimir> For the hard decision, the corrupt codeword can either fall on the no
Vladimir> man land, so you know that it can't be corrected; or it will be
Vladimir> aliased to the adjacent codeword and mistakenly decoded. For the soft
Vladimir> decision, the corrupt codeword will be decoded to the most likely
Vladimir> codeword which is going to be wrong.
Vladimir> I would say that the decoding fails completely, but I am not
>> sure. Could anybody explain this to me?, is there anyway to prevent
>> my decoding
>> from crashing when the received message contains more than 2t errors?
Vladimir> The standard practice is adding some integrity check for data, like
Vladimir> CRC, for example. So you know that the decoding process failed.
But doesn't the RS code already have pretty good detection
capabilities? Would adding a CRC really improve things more than,
say, adding another RS parity word or two?
Ray