On Sun, 15 Apr 2012 13:14:07 -0700 (PDT), dvsarwate <dvsarwate@yahoo.com> wrote:>On Apr 15, 1:38=A0pm, eric.jacob...@ieee.org (Eric Jacobsen) wrote: > > >> Dilip, that link appears to be broken. =A0 Is there a better one to that >> paper? > >Eric: > >Try this one: ><http://www.ifp.illinois.edu/~sarwate/pubs/Sarwate01High.pdf> > >or > ><http://www.icims.csl.uiuc.edu/~shanbhag/vips/publications/bma.pdf> > >For a recent implementation in MATLAB, see > ><http://www.mathworks.com/matlabcentral/fileexchange/34877-reed- >solomon-decoder-using-ribm-algorithm/content/RiBMDemo.m>That's useful, thanks!>and for what it's worth, I had e-mailed you a pdf copy of the paper >a few days ago with regard to BCH decoding that we were discussing. > >Dilip SarwateYes, I realized that as soon as I saw it. ;) Eric Jacobsen Anchor Hill Communications www.anchorhill.com
About Reed-Solomon
Started by ●April 14, 2012
Reply by ●April 15, 20122012-04-15
Reply by ●April 16, 20122012-04-16
On 04/15/2012 03:05 PM, dvsarwate wrote: [...]> http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.4985Hi Dilip, thanks again for the paper. I just went through the first part of it, which is, for me, the most interesting one. Being a novice in the field, the introduction part was really enlightening, for me. Anyhow, I'm used to see RS coding as product of an identity matrix, on top of a (partial) Vandermonde one, by the input data vector. Thus generating a systematic coding. The partial Vandermonde is usually made of rows (or columns) taken from the generic Vandermonde matrix of GF generators. That is the columns of: 1 1 1 ... 1 x0 x1 x2 ... xk-1 x0^2 x1^2 x2^2 ... xk-1^2 ... x0^k-1 x1^k-1 x2^k1 ... xk-1^k-1 Being in RAID GF(256), it seems that x0=1 (RAID-5) and x1=2 for RAID6. For 3 parities RAID it would be x2=4, I guess. Now, my question would be how are the GF generators xi chosen or calculated? Are they simply 2^j? I guess not... Sorry for the long boring post, I'm trying to explain my limited knowledge as clearly as I can. Thanks again, bye, -- piergiorgio
Reply by ●April 16, 20122012-04-16
On Apr 16, 2:08�pm, Piergiorgio Sartor <piergiorgio.sartor.this.should.not.be.u...@nexgo.REMOVETHIS.de> wrote:> On 04/15/2012 03:05 PM, dvsarwate wrote: > [...] > > >http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.4985 > > Hi Dilip, > > thanks again for the paper. > > I just went through the first part of it, which is, > for me, the most interesting one. > > Being a novice in the field, the introduction part > was really enlightening, for me. > > Anyhow, I'm used to see RS coding as product of an > identity matrix, on top of a (partial) Vandermonde > one, by the input data vector. > Thus generating a systematic coding. > > The partial Vandermonde is usually made of rows (or > columns) taken from the generic Vandermonde matrix of > GF generators. > That is the columns of: > > 1 � � � 1 � � 1 � � ... � �1 > x0 � � x1 � � x2 � �... xk-1 > x0^2 � x1^2 � x2^2 �... xk-1^2 > ... > x0^k-1 x1^k-1 x2^k1 ... xk-1^k-1 > > Being in RAID GF(256), it seems that x0=1 (RAID-5) and > x1=2 for RAID6. > For 3 parities RAID it would be x2=4, I guess. > > Now, my question would be how are the GF generators xi > chosen or calculated? > > Are they simply 2^j? I guess not... > > Sorry for the long boring post, I'm trying to explain > my limited knowledge as clearly as I can. > > Thanks again, > > bye, > > -- > > piergiorgioThe matrix used to encode a systematic RS code is not the same as the matrix used to compute the syndrome. Systematic encoding uses polynomial division; syndrome computation uses polynomial evaluation. Both processes are described in the paper you are reading. The notion of $2^i$ has no meaning in the Galois field used for computations. You need to understand some theory of finite fields to grasp what is going on. Dilip Sarwate Dilip Sarwate
Reply by ●April 17, 20122012-04-17
Hi Dilip, On 04/17/2012 01:34 AM, dvsarwate wrote: [...]> used for computations. You need to understand some > theory of finite fields to grasp what is going on.I think you're right, maybe I should dig a bit more into GF, but I was hoping in some practical "recipe" easy to understand. BTW, about GF, what could be good reference to start from? Thanks again, bye, -- piergiorgio
