Detection and Correction

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Data Communications &

Networking

ERROR DETECTION ANDERROR DETECTION AND

CORRECTIONCORRECTION

Chapter 8Chapter 8

First Semester 2007/2008


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ERROR DETECTION ANDERROR DETECTION ANDCORRECTIONCORRECTION

Types of Errors

Detection

Correction


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Data can be corrupted during transmission.

For reliable communication, errors must be

detected and corrected.

Note:Note:


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Types of Error

Single-Bit Error

Burst Error


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Data Communications &

Networking



Chapter 8Chapter 8

First Semester 2007/2008


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Types of Errors

Detection

Correction


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Data can be corrupted during transmission.

For reliable communication, errors must be

detected and corrected.

Note:Note:


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Types of Error

Single-Bit Error

Burst Error


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In a single-bit error, only one bit in the

data unit has changed.

Note:Note:

Single-Bit Error


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A burst error means that 2 or more bits

in the data unit have changed.

Note:Note:

Burst Error


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Error Detection

Redundancy

Parity Check

Cyclic Redundancy Check (CRC)

Checksum


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Error detection uses the concept of

redundancy, which means adding extrabits for detecting errors at the

destination.

Note:Note:


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Redundancy


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ErrorDetection methods


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Even-parity concept


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VERTICAL REDUNDANCY CHECK (VRC)


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In parity check, a parity bit is added to

every data unit so that the total numberof 1s is even

(or odd for odd-parity).

Note:Note:


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Example 1Example 1

Suppose the sender wants to send the word world. In

ASCII the five characters are coded as

1110111 1101111 1110010 1101100 1100100

The following shows the actual bits sent11101110 11011110 11100100 11011000 11001001


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Example 2Example 2

Now suppose the word world in Example 1 is received by

the receiver without being corrupted in transmission.

11101110 11011110 11100100 11011000

11001001

The receiver counts the 1s in each character and comes up

with even numbers (6, 6, 4, 4, 3). The data are accepted.


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Example 3Example 3

Now suppose the word world in Example 1 is corrupted

during transmission.

11111110 11011110 11101100 11011000

11001001


with even and odd numbers (7, 6, 5, 4, 4). The receiver

knows that the data are corrupted, discards them, and asks

for retransmission.


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Simple parity check can detect allSimple parity check can detect all

single-bit errors. It can detect burstsingle-bit errors. It can detect bursterrors only if the total number of errorserrors only if the total number of errors

in each data unit is odd.in each data unit is odd.

Note:Note:


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LONGITUDINAL REDUNDANCY CHECK

LRC

LRC 10101010

Data plus LRC

11100111 11011101 00111001 10101001

10101001

00111001

11011101

11100111

11100111 11011101 00111001 10101001 10101010


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Two-dimensional parity


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Figure 10.11 Two-dimensional parity-check code


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CRC generator and checker


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Data unit and checksum

SenderSenderReceiverReceiver


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The sender follows these steps:

The unit is divided into k sections, each of n bits.

All sections are added using ones complement to get the

sum.

The sum is complemented and becomes the checksum.

The checksum is sent with the data.

Note:Note:


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The receiver follows these steps:


All sections are added using ones complement to

get the sum.

The sum is complemented.

If the result is zero, the data are accepted: otherwise,

rejected.

Note:Note:


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Example 4Example 4

Suppose the following block of 16 bits is to be sent using a

checksum of 8 bits.

10101001 00111001

The numbers are added using ones complement

10101001

00111001

------------

Sum 11100010

Checksum 00011101

The pattern sent is 10101001 00111001 00011101


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Example 5Example 5

Now suppose the receiver receives the pattern sent in Example 7

and there is no error.

10101001 00111001 00011101

When the receiver adds the three sections, it will get all 1s, which,

after complementing, is all 0s and shows that there is no error.

10101001

00111001

00011101

Sum 11111111

Complement 00000000 means that the pattern is OK.


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Example 6Example 6

Now suppose there is a burst error of length 5 that affects 4 bits.

10101111 11111001 00011101

When the receiver adds the three sections, it gets

10101111

11111001

00011101

Partial Sum 1 11000101

Carry 1

Sum 11000110

Complement 00111001 the pattern is corrupted.


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Correction

Retransmission

Forward Error Correction

Burst Error Correction


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Hamming Code


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Data and redundancy bitsData and redundancy bits

Number ofdata bits

m

Number ofredundancy bits

r

Totalbits

m + r

11 2 3

22 3 5

33 3 6

44 3 7

55 4 9

66 4 10

77 4 11

12 ++ rmr

P iti f d d bit i H i d


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Positions of redundancy bits in Hamming code

0123

2,2,2,2

Redundancy bits calculation


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Example of redundancy bit calculation


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Error detection using Hamming code


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Burst error correction example


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In a single-bit error, only one bit in the

data unit has changed.

Note:Note:

Single-Bit Error


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A burst error means that 2 or more bits

in the data unit have changed.

Note:Note:

Burst Error


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Error Detection

Redundancy

Parity Check

Cyclic Redundancy Check (CRC)

Checksum


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Error detection uses the concept of

redundancy, which means adding extrabits for detecting errors at the

destination.

Note:Note:

Redundancy


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Redundancy

Error Detection methods


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ErrorDetection methods

Even parity concept


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Even-parity concept



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In parity check, a parity bit is added to

every data unit so that the total numberof 1s is even

(or odd for odd-parity).

Note:Note:


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Example 1Example 1

Suppose the sender wants to send the word world. In

ASCII the five characters are coded as

1110111 1101111 1110010 1101100 1100100

The following shows the actual bits sent

11101110 11011110 11100100 11011000 11001001


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Example 2Example 2

Now suppose the word world in Example 1 is received by

the receiver without being corrupted in transmission.

11101110 11011110 11100100 11011000

11001001


with even numbers (6, 6, 4, 4, 3). The data are accepted.


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Example 3Example 3

Now suppose the word world in Example 1 is corrupted

during transmission.

11111110 11011110 11101100 11011000

11001001


with even and odd numbers (7, 6, 5, 4, 4). The receiver

knows that the data are corrupted, discards them, and asks

for retransmission.


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LRC

LRC 10101010

Data plus LRC

11100111 11011101 00111001 10101001

10101001

00111001

11011101

11100111

11100111 11011101 00111001 10101001 10101010

Two-dimensional parity


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Two dimensional parity

Figure 10.11 Two-dimensional parity-check code


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gu e 0. wo d e s o p y c ec code

CRC generator and checker


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g

Data unit and checksum


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SenderSenderReceiverReceiver


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The sender follows these steps:


All sections are added using ones complement to get the

sum.

The sum is complemented and becomes the checksum.

The checksum is sent with the data.

Note:Note:


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The receiver follows these steps:


All sections are added using ones complement to

get the sum.

The sum is complemented.

If the result is zero, the data are accepted: otherwise,

rejected.

Note:Note:

E l 4E l 4


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Example 4Example 4

Suppose the following block of 16 bits is to be sent using a

checksum of 8 bits.

10101001 00111001

The numbers are added using ones complement

10101001

00111001

------------

Sum 11100010

Checksum 00011101

The pattern sent is 10101001 00111001 00011101

E l 5E l 5


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Example 5Example 5

Now suppose the receiver receives the pattern sent in Example 7

and there is no error.

10101001 00111001 00011101

When the receiver adds the three sections, it will get all 1s, which,

after complementing, is all 0s and shows that there is no error.10101001

00111001

00011101

Sum 11111111

Complement 00000000 means that the pattern is OK.

E l 6E l 6


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Example 6Example 6

Now suppose there is a burst error of length 5 that affects 4 bits.

10101111 11111001 00011101

When the receiver adds the three sections, it gets

10101111

11111001

00011101

Partial Sum 1 11000101

Carry 1

Sum 11000110

Complement 00111001 the pattern is corrupted.

C i


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Correction

Retransmission

Forward Error Correction

Burst Error Correction


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Hamming Code



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Number ofdata bits

m

Number ofredundancy bits

r

Totalbits

m + r

11 2 3

22 3 5

33 3 6

44 3 7

55 4 9

66 4 10

77 4 11

12 ++ rmr

Positions of redundancy bits in Hamming code


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0123

2,2,2,2



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Detection and Correction

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