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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