A recent paper out of Microsoft had an interesting twist on erasure
coding (separately encoding each half and then the entire thing once,
rather than the entire unit multiple times).
http://research.microsoft.com/en-us/um/people/yekhanin/papers/usenixatc_2012.pdf
it doesn't get at the math itself, but is something worth considering.
Best,
-Joe Buck
On 06/14/2013 01:13 PM, Martin Flyvbjerg wrote:
Dear Community
I am a young engineer (not software or math, please bare with me) with some
suggestions regarding erasure codes. I never used Ceph before or any other
distributed file system.
I stumped upon the suggestion for adding erasure codes to Ceph, as
described in this article
http://wiki.Ceph.com/01Planning/02Blueprints/Dumpling/Erasure_encoding_as_a_storage_backend
first I would like to say great initiative to add erasure codes to Ceph.
Ceph needs its own implementation and it have to be done right, I cannot stress
this enough, suggested software mentioned in that article would result in very
low performance.
Why?
Reed-Solomon is normally something regarded as being very slow compared to
other erasure codes, because the underlying Galois-Field multiplication is
slow. Please see video at usenix.org forexplanation.
The implementations of Zfec library and other suggested software the others
rely on the Vandermonde matrix, a matrix used in in Reed-Solomon erasure codes,
a faster approach would be to use the Cauchy-Reed-Solomon implementation.
Please see [1,2,3]
Although there is something even better, by using the Intel SSE2/3 SIMD
instructions it is possible to do the as fast as any other XOR based erasure
codes (RaptorQ LT-codes, LDPC etc.).
The suggested FECpp lib uses the optimisation but with a relative small
Galois-field only 2^8, since Ceph aimes at unlimited scalability increasing the
size of the Galois-Field would improve performance [4]. Of course the
configured Ceph Object Size and/or Stripe width have to be taken into account.
Please see
https://www.usenix.org/conference/fast13/screaming-fast-galois-field-arithmetic-using-sse2-extensions
The solution
Using the GF-Complete open source library [4] to implement Reed-Solomon in Ceph
in order to allow Ceph to scale to infinity.
James S. Plank the author of GF-complete have developed a library implementing
various Reed-Solomon codes called Jerasure.
http://web.eecs.utk.edu/~plank/plank/www/software.html
Jerasure 2.0 using the GF-complete artimetric based in Intel SSE SIMD
instructions, is current in development expected release august 2013. Will be
released under the new BSD license. Jerasure 2.0 also supports arbitrary
Galois-field sizes 8,16,32,64 or 128 bit.
The limit of this implementation would be the processors L2/L3 cache not the
underlying arithmetic.
Best Regards
Martin Flyvbjerg
[1] http://web.eecs.utk.edu/~plank/plank/papers/CS-05-569.pdf
[2] http://web.eecs.utk.edu/~plank/plank/papers/CS-08-625.pdf
[3] http://web.eecs.utk.edu/~plank/plank/papers/FAST-2009.pdf
[4] http://web.eecs.utk.edu/~plank/plank/papers/FAST-2013-GF.pdf
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