Solid State Storage (SSS) System Error Recovery

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Solid State Storage (SSS) System Error Recovery

• LHO 08

For NASA Langley Research Center
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Background

• NASA Langley Research Center is building a system
  to record streaming video and other data when the
  Space Shuttle docks with the Space Station.
• This data will be used to develop algorithms that
  will enable the next generation of the space
  station to perform autonomous docking.
• Due to the harsh environment in space the data
  will be stored in a RAID array of solid state
  SATA drives with the capability of recovering
  data even if two drives fail.
• This Solid State Storage (SSS) system is being
  developed at VCU.
• We will look at the that portion of the system
  that deals with drive error recovery.

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Proposed SSS system Overview
To data recorder
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SSS Data Recovery

• The Solid State Storage (SSS) system will consist
  of six solid state data drives. The discussion
  will be directed to this specific configuration.
• The data will be sector striped across these six
  drives.
• A modified RAID 6 system capable of recovering
  data from two corrupted sectors in a stripe is
  proposed.
• Optimized for long single-thread transfers that
  are multiples of the entire stripe.

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RAID 5

• To illustrate concepts and implications consider
  a RAID 5 implementation.
• RAID 5 uses striped array with rotating parity.
• Optimized for short, multithreaded transfers.
• Capable of recovering from a single drive
  failure.

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RAID 5 system consisting of three data drives and
rotating parity. Four stripes for sectors A, B,
C, and D are shown.
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Rotating Parity

• Why rotating parity?
• The following steps are necessary to update a
  single data sector in a stripe.
• The old data sector and the parity sector for the
  stripe must be read.
• Compute the new parity using the new data sector,
  old data sector, and old parity.
• Write new data sector and new parity sector.
• Thus, to write to a data sector both the data
  sector and parity sector must be read and
  written.
• Since there are many data drives a fixed parity
  drive would accessed much more frequently than a
  data drive.
• This excessive access of a single parity drive is
  avoid by rotating parity across all drives.

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Rotating parity not needed in SSS

• The SSS is required to store long data streams.
  Not random sectors.
• Make the size of these streams a multiple of the
  stripe size.
• An entire stripe with parity will be buffered.
• The entire stripe with party will be
  simultaneously written to all drives.
• It is not necessary to first read the drives.
• The SSS will always read and write entire
  stripes.
• Easier to implement.
• Faster access.

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Parity

• Parity encoding is given by
• Where Di represent a data byte in a sector on
  drive i.
• If both sides of the above equation are exclusive
  ored with P, then
• D5 for example can be recovered by

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Parity problem

• Using parity it is easy to recover data on a
  single drive if we know that drive is bad.
• We may have data corruption on a drive without
  without the entire drive failing.
• Undetectable based on parity alone.
• Propose to include a 32-bit CRC in sector.
• Simple to implement.
• Less than 1 overhead.
• In RAID 6 will ensure as long as a stripe has no
  more than two bad sectors the data in that stripe
  can be recovered.

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Key Conclusions

• Write data as entire stripes.
• Used fixed parity drive.
• Include sector CRC.

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Raid 6 (modified)

• Use two fixed parity drives (P and Q).
• Data can be recovered if two sectors in a stripe
  are corrupted.
• P parity is the same as RAID 5 (simple XOR).
• Easy to encode and easy to recover data.
• Q parity is more complicated.

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Q parity encoding
The Q parity is a Reed-Solomon code given by
Where ? is Galois Field (GF) multiplication and
gi is a constant. For i lt 8 it turns out that gi
2i. For larger i, it not as simple. For example
g8 29. But for the SSS application Q simplifies
to
The problem is how to compute the GF
multiplication.
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GF multiplication

• In ordinary arithmetic multiplication can be
  accomplished summing the logs and taking the
  inverse log.
• GF multiplication is typically accomplished using
  lookup tables to find the GF log and inverse log.
  The addition in modulo 255.
• See Xilinx application note XAPP731 Hardware
  Accelerator for RADD 6 Parity Generation / Data
  Recovery Controller.

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Examples
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Examples
Note A?B 0 if A 0 or B 0. This is a
special case and cannot be computed using
logs. It is also worth noting that A?1 A. This
does follow from using logs since logGF(0x01) 0.
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Elaboration on Galois Field Mathematics

• Évariste Galois (1832)
• Established many of the ideas of group theory.
• Left only sixty pages of mathematical writings.
• Mortally wounded in a duel at age 20.
• Most of his major centrifugations stem from a
  letter written the night before the duel.
• His work has had great impact.
• Provides powerful tool for investigating
  fundamental mathematical problems.
• Roots of algebraic equations.
• GF theory provides simple proof that an angle
  cannot be trisected using only compass and
  unmarked straightedge.
• This had baffled mathematicians since the time of
  Euclid.
• Recently applied to computer design and
  data-communication systems.

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Galois Field Mathematics

• A Galois Field is a algebraic structure ltG,?,?gt
  where G is a set consisting of 2n elements, ? is
  addition mod 2 (bit wise XOR) and ? is GF
  multiplication. Math similar to ordinary
  arithmetic.
• ? and ? is commutative and associative.
• Distributive such that
• We are only concerned with GF(28) where the set G
  has 256 elements. We will use a hex byte to
  specify the elements.
• Then A ? A 0x00, A ? 0x00 0x00, A ? 0x01 A

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GF(28)

• The GF log look up tables are generates based on
  what in GF theory is called a primitive
  polynomial. Primitive polynomials have certain
  properties that lead to the error correction
  techniques.
• GF(28) is generated using the primitive
  polynomial
• This is the same primitive polynomials use to
  determine the feed back path for an 8-bit maximum
  count linear feedback shift registers (LFBSRs).
• The LFBSR can be use to perform GF
  multiplication.

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The 8 bit LFBSR
Q0 Q1 Q2
Q3 Q4 Q5 Q6 Q7
Or reversing order so that the most significant
bit is at the left
A shift has the same effect as ? 2. In VHDL Q lt
Q(6) Q(5) Q(4) (Q(3) XOR Q(7))
(Q(2) XOR Q(7)) (Q(1) XOR Q(7)) Q(0) Q(7)
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Galois Field Division