Re: Announcing cdrskin-0.7.2

Hi,

> it seems as if the
> internet has enough information to get to a solution.

Yes, it has.

A new source module ecma130ab was committed
to libburn SVN yesterday.
I would appreciate if you had a look at the
explanations at lines 8 to 115 whether you find
any mistakes or gaps.
  http://libburnia-project.org/browser/libburn/trunk/libburn/ecma130ab.c


By help of Norbert Preining i found a document
about Reed-Solomon for RAID applications by
James S. Plank which provided me with the
theoretical background to understand ECMA-130
Annex A.
The resulting implementation is unoptimized and
needs about 50 % more time than the old one which
was labeled "borrowed HEAVILY from cdrdao".

ECMA-130 Annex B, the scrambler, was easier to
learn. Only obstacle was that the diagram in
ECMA-130 shows a 16 bit register in Fibonacci
form whereas the text talks of a 15 bit register
with a 15 bit polynomial that refers to the
Galois form. Well, if one removes the surplus
box from the Fibonacci then it is trivial to
implement. (Thanks to a company named New Wave
Instruments for an overview of Linear Feedback
Shift Register nomenclature.)

I ran my whole hard disk content through a
comparison of old and new output. It matched.
Whether the old output exactly complies to
ECMA-130 would be subject to a real test case
for raw CD writing.
I learned that Annex A is needed to encode a
data block into an audio-sized sector. Annex B
is needed to prepare an audio-sized sector for
raw writing.
Both tasks are performed by the drive if the
MMC defined write modes for data and audio are
used.


> Gallois Fields have size p^m where p is a prime (in our case, 2).

... and weird arithmentics (at least with p=2).
Plus is minus, logarithms are exact, powers of x
behave like elements of modulo prime groups. 
(I seem to have backed out of algebra just before
finite fields became topic.)


> I admit that I'm shooting from the hip here.

Good shot.

The only thing that i have to amend is that the
road via Fourier turned out to be a diversion.
All statements in ECMA-130 Annex A refer already
to the finite field aspect of Reed-Solomon. (I
did not have to learn how frequencies and finite
fields are related. It has to be expected that
there is funny arithmetics, too.)


Have a nice day :)

Thomas


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