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Adds more details about Quad Parity.

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Andrea Mazzoleni 2013-09-11 21:30:21 +02:00
parent 32130a4bdf
commit 7e0b93caef
1 changed files with 21 additions and 8 deletions
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raid.c
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@ -816,22 +816,34 @@ void raid_gen(unsigned level, unsigned char** buffer, unsigned diskmax, unsigned
/**
* The data recovering is based on paper "The mathematics of RAID-6" [1],
* that covers the RAID5 and RAID6 computation in the Galois Field GF(2^8)
* with the primitive polinomial x^8 + x^4 + x^3 + x^2 + 1 (285 decimal),
* using generators "1" and "2".
* with the primitive polynomial x^8 + x^4 + x^3 + x^2 + 1 (285 decimal),
* using parity generators "1" and "2".
*
* To support RAIDTP (Triple Parity), we use an extension of the same approach,
* described in the paper "Multiple-parity RAID" [2], with the additional
* generator "4".
*
* also described in the paper "Multiple-parity RAID" [2], with the additional
* parity generator "4".
* This method is also the same used by ZFS to implement its RAIDTP
* support.
*
* Note that the same extension is not possible for Quad Parity because
* in the approach used in the paper we don't have the guarantee to have a
* system of independent linear equations, and for Quad Parity in some cases
* in the approach used in the paper we don't have the guarantee to always have
* a system of independent linear equations, and for Quad Parity in some cases
* the system is not solvable.
*
* Using the primitive polynomial 285, Quad Parity works for up to 21 disks
* with parity generators "1,2,4,8". Changing polynomial to 391, it works for
* up to 27 disks with the same parity generators.
* Using different parity generators like "1,7,53,139" it's possible to
* make it working for up to 33 disks. But no more.
*
* A general method working for Quad Parity and more, can be found in [3]
* and corrected in [4], but with a slower computational performance.
* and corrected in [4], but with a slower computational performance,
* because the coefficients of the equations are arbitrarely chosen,
* and not derived from parity generators.
* This means that you need to use multiplication tables to implement the
* syndrome computation, instead of the fast approach described in [1].
* Note anyway, that there is also a way to implement multiplication tables
* in a very fast way with SSE instructions [5].
*
* In details, Triple Parity is implemented for n disks Di, computing
* the syndromes P,Q,R with:
@ -886,6 +898,7 @@ void raid_gen(unsigned level, unsigned char** buffer, unsigned diskmax, unsigned
* [2] David Brown, "Multiple-parity RAID", 2011
* [3] James S. Plank, "A Tutorial on Reed-Solomon Coding for Fault-Tolerance in RAID-like Systems", 1999
* [4] James S. Plank, Ying Ding, "Note: Correction to the 1997 Tutorial on Reed-Solomon Coding", 2003
* [5] James S. Plank, "Screaming Fast Galois Field Arithmetic Using Intel SIMD Instructions", 2013
*/
/**