Decoding RSPC (Reed Solomon Product Code) 
Author Message
 Decoding RSPC (Reed Solomon Product Code)

Hi,

I'm writing a prog (VHDL or C) to enable block encoding and decoding of CD
sectors.  In the ECC (error correction coding) field, RSPC(Reed Solomon
Product Code) is used. The RSPC is a product code over GF(2^8) producing P
and Q parity bytes.  The GF(2^8) field is generated by the primitive
polynomial
P(x) = x^8 + x^4 + x^3 + x^2 + 1
The P parities are (26,24) RS codeword over GF(2^8) and the Q parities are
(45,43) RS codeword over GF(2^8).

My question is: How can I write the encoding and decoding algorithm for the
ECC field?? The RS used are non standard RS codes (n,k) in which n is
usually n=2^m -1 which m=8 in this case...
I tried to look for more info from books but it is really limited... I came
across some books saying that conventional RS decoding can be used.. that is
the berlekamp, Peterson and Weldon algorithm.  But I see no connection
between them coz the derivation is based on a fundamental which is
different.

Pls enlighten... by providing some books, paper, web site or perhaps
explanation of theory behind them...  Thank you very much!!

Happy Millenium 2000!!

MKYap



Sat, 22 Jun 2002 03:00:00 GMT  
 Decoding RSPC (Reed Solomon Product Code)
Try http://www.fokus.gmd.de/research/cc/mobra/products/fec/ .  They have
some utilities (genenc and genrs) which, given m, n, and k as paramerters,
will generate a synthesizable VHDL design.  Perhaps a good starting point...

Good Luck,
John

Quote:

>Hi,

>I'm writing a prog (VHDL or C) to enable block encoding and decoding of CD
>sectors.  In the ECC (error correction coding) field, RSPC(Reed Solomon
>Product Code) is used. The RSPC is a product code over GF(2^8) producing P
>and Q parity bytes.  The GF(2^8) field is generated by the primitive
>polynomial
>P(x) = x^8 + x^4 + x^3 + x^2 + 1
>The P parities are (26,24) RS codeword over GF(2^8) and the Q parities are
>(45,43) RS codeword over GF(2^8).

>My question is: How can I write the encoding and decoding algorithm for the
>ECC field?? The RS used are non standard RS codes (n,k) in which n is
>usually n=2^m -1 which m=8 in this case...
>I tried to look for more info from books but it is really limited... I came
>across some books saying that conventional RS decoding can be used.. that
is
>the berlekamp, Peterson and Weldon algorithm.  But I see no connection
>between them coz the derivation is based on a fundamental which is
>different.

>Pls enlighten... by providing some books, paper, web site or perhaps
>explanation of theory behind them...  Thank you very much!!

>Happy Millenium 2000!!

>MKYap



Sat, 22 Jun 2002 03:00:00 GMT  
 Decoding RSPC (Reed Solomon Product Code)
The following book might be of help, although it is out of print. Perhaps
you can find it in a good library:

Schouhamer Immink, K.A.: Coding techniques for digital recorders.
   Prentice Hall, New-York etc. 1991  

You can also check the following web site which describes some research on
RS decoders on FPGAs:

  http://www.ee.byu.edu/~ahlquist

Finally, if you click the "Recent Publications" button at our web site at

  http://www.ece.wpi.edu/Research/crypt

you will find an article by Rosner/Paar about arithmetic for RS decoders
on FPGAs.

Hope that is of some help,

Christof

! WORKSHOP ON CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS (CHES 2000) !
!                   WPI, August 17 & 18, 2000                         !
!          http://www.ece.wpi.edu/Research/crypt/ches                 !

***********************************************************************
                 Christof Paar,  Assistant Professor
          Cryptography and Information Security (CRIS) Group
      ECE Dept., WPI, 100 Institute Rd., Worcester, MA 01609, USA

fax:(508) 831 5491  www: http://www.ece.wpi.edu/People/faculty/cxp.html
***********************************************************************

Quote:

> >Hi,

> >I'm writing a prog (VHDL or C) to enable block encoding and decoding of CD
> >sectors.  In the ECC (error correction coding) field, RSPC(Reed Solomon
> >Product Code) is used. The RSPC is a product code over GF(2^8) producing P
> >and Q parity bytes.  The GF(2^8) field is generated by the primitive
> >polynomial
> >P(x) = x^8 + x^4 + x^3 + x^2 + 1
> >The P parities are (26,24) RS codeword over GF(2^8) and the Q parities are
> >(45,43) RS codeword over GF(2^8).

> >My question is: How can I write the encoding and decoding algorithm for the
> >ECC field?? The RS used are non standard RS codes (n,k) in which n is
> >usually n=2^m -1 which m=8 in this case...
> >I tried to look for more info from books but it is really limited... I came
> >across some books saying that conventional RS decoding can be used.. that
> is
> >the berlekamp, Peterson and Weldon algorithm.  But I see no connection
> >between them coz the derivation is based on a fundamental which is
> >different.

> >Pls enlighten... by providing some books, paper, web site or perhaps
> >explanation of theory behind them...  Thank you very much!!

> >Happy Millenium 2000!!

> >MKYap



Sun, 23 Jun 2002 03:00:00 GMT  
 Decoding RSPC (Reed Solomon Product Code)


Quote:
> Hi,

> I'm writing a prog (VHDL or C) to enable block encoding and decoding
of CD
> sectors.  In the ECC (error correction coding) field, RSPC(Reed
Solomon
> Product Code) is used. The RSPC is a product code over GF(2^8)
producing P
> and Q parity bytes.  The GF(2^8) field is generated by the primitive
> polynomial
> P(x) = x^8 + x^4 + x^3 + x^2 + 1
> The P parities are (26,24) RS codeword over GF(2^8) and the Q parities
are
> (45,43) RS codeword over GF(2^8).

> My question is: How can I write the encoding and decoding algorithm
for the
> ECC field?? The RS used are non standard RS codes (n,k) in which n is
> usually n=2^m -1 which m=8 in this case...
> I tried to look for more info from books but it is really limited... I
came
> across some books saying that conventional RS decoding can be used..
that is
> the berlekamp, Peterson and Weldon algorithm.  But I see no connection
> between them coz the derivation is based on a fundamental which is
> different.

> Pls enlighten... by providing some books, paper, web site or perhaps
> explanation of theory behind them...  Thank you very much!!

You're dealing with shortened Reed-Solomon codes; you may not find much
that specifically describes their encoding and decoding beacause it is
almost the same as the non-shortened version. For the encoder, encode as
a generic cyclic code over GF(2^8). For the decoding the Euclidean
Algoithm decoder will work for the shortened codes the same way it would
for the non-shortened ones with n=your codeword length instead of 2^m-1.
I'm sure the Berlekamp-Massey algorithm will also work with only minor
modifications.

Jacob Hirbawi.

Sent via Deja.com http://www.deja.com/
Before you buy.



Fri, 28 Jun 2002 03:00:00 GMT  
 Decoding RSPC (Reed Solomon Product Code)
Hi!

So I'm shortening the RS(31,29) to become RS(26,24)... for encoding and
decoding, the feedback arithmetic addition and multiplication is based on
GF(2^8) so there shouldn't be any prob....

Quite a headache for me, I can't even get the syndrome correct..

for many of the downloaded progs that support shortened RS, when i changed
the nn ( i.e. RS (nn,kk,8) )from 31 to 26, the result wouldn't be correct
unless the condition nn = 2^m-1 is met.. I manually  generate the GF(2^8)
and use it for encoding and decoding.. well, still the same... i can't get
the correct RS parity bytes...    Any idea??

Would appreciate if someone can shed some light on it.

MKYap


Quote:
> Hi,

> Thanks for all the responses... I have got hold of the few RS codec
> programs, still playing ard with them...

> How does the actual encoding and decoding process vary with the shortened
RS
> code, say RS (26,24)? Can I just feed in the data byte(m=8) into the
encoder
> (shift registers) as per normal? ie. shift in 24 data bytes ( and shift
> another 2 empty bytes??) and the register content is the 2 parity bytes?

> I have a few sets of sample answer but I can never get to the answer no
> matter how i shift...

> btw, how do u shorten the normal RS(31,27) (double error correcting??) to
> RS(26,24) ?

> Thanks for all helps/advice  :-)

> MKYap




> > > Hi,

> > > I'm writing a prog (VHDL or C) to enable block encoding and decoding
> > of CD
> > > sectors.  In the ECC (error correction coding) field, RSPC(Reed
> > Solomon
> > > Product Code) is used. The RSPC is a product code over GF(2^8)
> > producing P
> > > and Q parity bytes.  The GF(2^8) field is generated by the primitive
> > > polynomial
> > > P(x) = x^8 + x^4 + x^3 + x^2 + 1
> > > The P parities are (26,24) RS codeword over GF(2^8) and the Q parities
> > are
> > > (45,43) RS codeword over GF(2^8).

> > > My question is: How can I write the encoding and decoding algorithm
> > for the
> > > ECC field?? The RS used are non standard RS codes (n,k) in which n is
> > > usually n=2^m -1 which m=8 in this case...
> > > I tried to look for more info from books but it is really limited... I
> > came
> > > across some books saying that conventional RS decoding can be used..
> > that is
> > > the berlekamp, Peterson and Weldon algorithm.  But I see no connection
> > > between them coz the derivation is based on a fundamental which is
> > > different.

> > > Pls enlighten... by providing some books, paper, web site or perhaps
> > > explanation of theory behind them...  Thank you very much!!

> > You're dealing with shortened Reed-Solomon codes; you may not find much
> > that specifically describes their encoding and decoding beacause it is
> > almost the same as the non-shortened version. For the encoder, encode as
> > a generic cyclic code over GF(2^8). For the decoding the Euclidean
> > Algoithm decoder will work for the shortened codes the same way it would
> > for the non-shortened ones with n=your codeword length instead of 2^m-1.
> > I'm sure the Berlekamp-Massey algorithm will also work with only minor
> > modifications.

> > Jacob Hirbawi.

> > Sent via Deja.com http://www.deja.com/
> > Before you buy.



Sat, 29 Jun 2002 03:00:00 GMT  
 
 [ 5 post ] 

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