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Hamming Code - Computer Architecture - Lecture Slides, Slides of Introduction to Database Management Systems

Himgiri Zee UniversityIntroduction to Database Management Systems

Hamming Code, Code Length, Number of information symbols, Number of parity check symbols, CRC Generator, Polynomial, RAID Level, Performance of RAID Levels are the topics professor discussed in class.

Typology: Slides

2011/2012

Uploaded on 11/03/2012

dharmaraaj
dharmaraaj 🇮🇳

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(68)

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bg1
1
Received vector
buffer register r
Syndrome calculation circuit
Error-pattern-detecting circuit
…
…
…
+
+
+
Corrected Output
v0
r1
r0
v1
e1
e0
rn-1
vn-1
en-1
sn-1
s1
s0
rn-1
r1
r0
r
General
Decoder
for a
Linear
Block
Code
Docsity.com
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13
pf14
pf15
pf16
pf17

Partial preview of the text

Download Hamming Code - Computer Architecture - Lecture Slides and more Slides Introduction to Database Management Systems in PDF only on Docsity!

1

Received vector buffer register r

Syndrome calculation circuit

Error-pattern-detecting circuit

Corrected Output

v (^0)

r 0 r (^1)

v (^1)

e 0 e 1

r (^) n-

v (^) n-

en-

s 0 s 1 s^ n-

r 0 r 1 r (^) n-

r

General

Decoder

for a

Linear

Block

Code

2

Hamming Code

• First class of linear codes devised

for error correction

4

Example

For m=3,

• The parity-check matrix of

Hamming code is (7,4) linear

code.

5

Example: Encode 1011 Using the

Hamming Code and Odd Parity

  • Insert the data bits: P 1 P 2 1 P 4 0 1 1
  • P 1 is computed from P 1 ⊕ D 3 ⊕ D 5 ⊕ D 7 = 1, so

P 1 = 1.

  • P 2 is computed from P 2 ⊕ D 3 ⊕ D 6 ⊕ D 7 = 1, so

P 1 = 0.

  • P 4 is computed from P 1 ⊕ D 5 ⊕ D 6 ⊕ D 7 = 1, so

P 1 = 1.

  • The final encoded number is 1 0 1 1 0 1 1.

7

b 0 b 1 b 2 b 3 b 4 b 5 b 6 b 7 b 8 b 9 b 10 b 11 b 12 b 13 b 14 b 15

Data

CRC Generator Based on the

Polynomial x16 + x12 + x5 + 1

8

  • 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.

10

RAID Level 0

• Not a true member of the RAID

family.

• Does not include redundancy to

improve performance.

11

  • In few applications, capacity and

performance are primary

concerns than improved reliability.

  • So RAID level 0 is used in such

applications.

13

Performance of RAID Levels

Performance of RAID Levels

depends upon two factors:

  • Request pattern of the host system
  • Layout of the data

14

b (^0)

…

b (^2)

…

b (^1)

…

b (^3)

…

f 0 (b)

f 1 (b)

…

f 2 (b)

…

RAID Level 2

16

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

17

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.

19

Block

Block

Block

Block

Block

Block

Block

Block

Block

Block

Block

Block

Block

Block

Block

Block

RAID Level 4

P(8-11)

P(4-7)

P(12-15)

P(0-3)

20

Block

Block Block

Block

Block

Block

Block

Block

Block

Block

Block

Block

Block

Block

Block

Block

RAID Level 5

P(16-19)

P(4-7) P(8-11) P(12-15)

P(12-15)

Block

Block

Block Block …

P(0-3)