CPR E 545: Fault Tolerant Systems

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CPR E 545 Fault Tolerant Systems

• Advances in RAID Architecture
• By Mohammad Fraiwan

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Summary of RAID Levels
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RAID-6

• Block-level striping with dual distributed
  parity.
• Two sets of parity are calculated.
• Better fault tolerance
• Can handle two faulty disks.
• Writes are slightly worse than 5 due to the added
  overhead of more parity calculations.
• May get better read performance than 5 because
  data and parity is spread into more disks.
• If one disks fail, then levels 6 becomes level 5.

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Reed-Solomon ECC 3

• A coding scheme that works by
• Constructing a polynomial from the data.
• Construct an over-sampled plot of the original
  polynomial.
• The redundant information in the over-sampled
  data allows the original polynomial to be
  reconstructed even in the face of errors.

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Method Overview

• Data is stored (send) as an encoded block.
• The total number of m-bit symbols in the encoded
  block is n2m-1.
• Example a Reed-Solomon code operating on 8-bit
  symbols has n28-1 255 symbols per block.
• There are n-k parity symbols of m bits each.

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Method Overview cont.

• A commonly used code encodes k 223 8-bit data
  symbols plus 32 8-bit parity symbols in a n
  255-symbol block.
• The codes are denoted as (n,k) codes. In the
  above case (n,k) (255,223).
• An (n,k) code is capable of correcting (n-k)/2
  symbol errors per block.

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Method Overview Cont.

• The scheme encodes the block as points in a
  polynomial plotted over a finite field.
• A Finite field is a field that contains finitely
  many elements.
• The coefficients of the polynomial are the data
  symbols of the block.
• The plot over-determines the coefficients, which
  can be recovered from subsets of the plotted
  points.
• a Reed-Solomon code can bridge a series of errors
  in a block of data to recover the coefficients of
  the polynomial that drew the original curve.

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Properties of the Reed-Solomon Code

• The measure of redundancy in the block, n-k,
  determines the error correction capability.
• If the locations of the erroneous symbols are not
  known in advance, then a Reed-Solomon code can
  correct up to (n-k)/2 erroneous symbols.
• Reed-Solomon codes especially well-suited to
  applications where errors occur in bursts.
• This is because it does not matter to the code
  how many bits in a symbol are in errorif
  multiple bits in a symbol are corrupted it only
  counts as a single error.

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RS Applications

• Storage devices (including tape, Compact Disk,
  DVD, barcodes, etc)
• Wireless or mobile communications (including
  cellular telephones, microwave links, Satellite,
  etc)
• Digital television / DVB
• High-speed modems such as ADSL, xDSL, etc.
• Reed Solomon is a poor choice in applications
  with random number of single bit errors.

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History of Reed-Solomon codes

• Invented in 1960 by Irving S. Reed and Gustave
  Solomon. Members of MIT Lincoln Laboratory.
• The article title was "Polynomial Codes over
  Certain Finite Fields.
• Digital technology was not advanced enough to
  implement the concept.
• The key to application of Reed-Solomon codes was
  the invention of an efficient decoding algorithm
  by Elwyn Berlekamp, a professor of electrical
  engineering at the University of California,
  Berkeley.

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RAID-7

• Proprietary RAID design trademark of Storage
  Computer Corporation .
• Asynchronous, cached striping with dedicated
  parity.
• based on concepts used in RAID levels 3 and 4.
• Greatly enhanced to address some of the
  limitations of those levels.
• Extensive Caching and a specialized real-time
  processor for managing the array asynchronously.

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RAID-7 cont.

• Best access concurrency.
• Best throughput.
• Good fault tolerance.
• Expensive solution made and supported by one
  company.

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Nested RAID Levels

• Single RAID levels have distinct advantages and
  disadvantages.
• It is possible to get some of the advantages of
  more than one RAID level by designing arrays that
  use a combination of multiple levels.
• Nested RAID levels typically provide better
  performance than single levels, but at some cost.

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RAID-10 Striped Mirroring

• RAID 10 Striping mirroring
• A striped array of RAID 1 arrays
• High performance of RAID 0, and high tolerance of
  RAID 1 (at the cots of doubling disks).

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Comparing RAID levels
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Comparing RAID levels 1
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• 1 Comparing RAID Levels, http//www1.us.dell.com
  /content/topics/global.aspx/power/en/ps1q02_long?c
  uslensgen
• 2 RAID Levels http//www.pcguide.com/ref/hdd/per
  f/raid/levels/index.htm
• 3 Reed-Solomon error correction
  http//www.4i2i.com/reed_solomon_codes.htm