1. … General Decoder for a Linear Block Code … …
Received vector
buffer register r r … r0 r1
rn-1
Syndrome calculation circuit
General
Decoder
for a
Linear
Block
Code … s0 s1
sn-1
Error-pattern-detecting circuit … e0 e1
en-1 r0 r1
rn-1 + + + v0 v1
vn-1
Corrected Output

2. CS501 Advanced Computer Architecture
Lecture 33
Dr.Noor Muhammad Sheikh

3. Review

4. Operating System Interface

5. Parity Check Code

6. Hamming code

7. Redundant Array of Independence Disk

8. Hamming Code
First class of linear codes devised for error correction

9. For any positive integer m<=3 ,a Hamming code with following parameters exists:
Code Length:
n=2m-1
Number of information symbols:
k = 2m-1-m
Number of parity-check symbols:
n – k = m

10. Example For m=3, The parity-check matrix of
Hamming code is (7,4) linear code.

11. Example: Encode 1011 Using the Hamming Code and Odd Parity
Insert the data bits: P1 P2 1 P
P1 is computed from P1 Å D3 Å D5 Å D7 = 1, so P1 = 1.
P2 is computed from P2 Å D3 Å D6 Å D7 = 1, so P1 = 0.
P4 is computed from P1 Å D5 Å D6 Å D7 = 1, so P1 = 1.
The final encoded number is

12. Example : Compute the Odd Parity SECDED Encoding of the 8-bit value 01101011
The 8 data bits would have 5 parity bits added to them to make the 13-bit value
P0 P1 P2 0 P P
P1 = 0, P2 = 1, P4 = 0, and P8 = 0
we can compute that P0, overall parity, = 1, giving the encoded value:

13. CRC Generator Based on the Polynomial x16 + x12 + x5 + 11 2 3 4 5 6 7 8 9 1 1 1 1 2 1 3 1 4 1 5
Data

14. The number and position of XOR gates is determined by the polynomial.
CRC does not support error correction but the CRC bits generated can be used to detect multibit errors.
The CRC results in extra CRC bits, which are appended to the data word and sent along.
The receiving entity can check for errors by recomputing the CRC and comparing it with the one that was transmitted.

15. RAID Level 0 … … … … Strip8 Strip4 Strip12 Strip0 Strip1 Strip10

16. RAID Level 0 Not a true member of the RAID family.
Does not include redundancy to improve performance.

17. In few applications, capacity and performance are primary concerns than improved reliability.
So RAID level 0 is used in such applications.

18. RAID Level 0
The user and system data are distributed across all the disks in the array.
Notable advantage over the use of a single large disk.
Two requests can be issued in parallel, requesting the I/O queuing time.

19. Performance of RAID Levels
Performance of RAID Levels depends upon two factors:
Request pattern of the host system
Layout of the data

20. RAID Level 2 b0 … b1 … b2 … b3 …
f0 (b) …
f1(b) …
f2(b) …

21. RAID Level 3 b0 … b1 … b2 … b3 …
P (b) …

22. RAID 2 and RAID 3 Make use of parallel access techniques.
All member disks participate in execution of every request.
Spindles of the individual drives are synchronized

23. RAID 2 and RAID 3 Data striping is used.
Strips are as small as a single byte or word.
In RAID 2, error-correcting code is calculated across corresponding bits on each data disk.

24. Difference between RAID2 and RAID 3
RAID 3 requires only a single redundant disk.
Instead of an error-correcting code, a simple parity bit is computed for the set of individual bits in RAID 3

25. RAID Level 4 … … … … … Block8 Block4 Block12 Block0 Block1 Block2
P(8-11)
P(4-7)
P(12-15)
P(0-3) …
Block5
Block6
Block7
Block9
Block10
Block11
Block13
Block14
Block15 … … …

26. RAID Level 5 … … … … … Block8 Block4 Block12 Block0 Block1 P(12-15)

27. RAID Level 4 Make use of independent access technique.
Both RAID levels 4 and 5 are suitable for those applications which require high I/O requests rates, and less suitable which require high data rate transfer.
Data striping is used.
A bit-by-bit parity strip is calculated across corresponding strip on each data disk.

28. RAID 4
Involves a write penalty when an I/O write request of small size is performed.
To calculate the new parity, the array management software must read the old user parity strip.

29. RAID 4 Each strip involves two reads and two writes.
For large size I/O writes, parity is easily computed by calculation using only the new data bits.
Parallel drives can be updated in parallel with data drives.