Error Detection and Correction 4
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Transcript of Error Detection and Correction 4
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Data Communication BSIT 2nd BZUpages.COM
Error Detection
and
Correction
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Types of ErrorTypes of Error
Single-Bit Error
Burst Error
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Single-bit error
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Burst error of length 5
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DETECTIONDETECTION
Parity Check
Cyclic Redundancy Check (CRC)
Checksum
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Binary division in a CRC
generator
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Binary division in CRC
checker
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A polynomial
representing a divisor
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Standard polynomialsStandard polynomials
Name Polynomial Application
CRCCRC--88 x8 + x2+ x+ 1 ATM header
CRCCRC--1010 x10 + x9+ x5+ x4+ x2 + 1 ATM AAL
ITUITU--1616 x16 + x12 + x5+ 1 HDLC
ITUITU--3232x32 + x26+ x23 + x22 + x16 + x12 + x11 + x10
+ x8 + x7 + x5 + x4 + x2 + x+ 1LANs
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Example 7Example 7
Supposethe
following
block
o
f 16 bitsis
to
besen
tusing
a
checksumof 8 bits.
10101001 00111001
Thenumbers are added usingonescomplement
10101001
00111001
------------
Sum 11100010
Checksum 00011101
Thepatternsent is 10101001 00111001 00011101
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Example 8Example 8
Now
suppose
thereceiver
receives
thep
attern
sen
tin
Example
7
and thereisnoerror.
10101001 00111001 00011101
When thereceiveradds the threesections,it willget all 1s,which,
aftercomplementing,is all 0s and shows that thereisnoerror.
10101001
00111001
00011101
Sum 11111111
Complement 00000000 Thepatternis OK
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Example 9Example 9
Now
suppose
there
is
a burs
terror
o
fleng
th 5 that affec
ts
4 bits.
10101111 11111001 00011101
When thereceiveradds the threesections,it gets
10101111
11111001
00011101
PartialSum 1 11000101
Carry 1
Sum 11000110
Complement 00111001 the pattern is corrupted.
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CorrectionCorrection
Retransmission
Forward Error Correction
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This pair of bytes has a
Hamming distance of 3:
Hamming code can detect - D(min) 1 errors
Hamming code can correct - errors
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HAMMI
NG(7,4)
1 2 3 4 5 6 7
P1 P2 P3
1 2 3 4 5 6 7
P1 P2 D1 P3 D2 D3 D4
Parity bits - 2^n th bits
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DATA BIT -1011
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WITHOUT ERROR
WITH ERROR
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DECODING
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THANKYOU