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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
ERROR DETECTION ANDERROR DETECTION AND
CORRECTIONCORRECTION
Chapter 8Chapter 8
First Semester 2007/2008
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ERROR DETECTION ANDERROR DETECTION AND
CORRECTIONCORRECTION
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
The receiver counts the 1s in each character and comes up
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:
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.
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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Redundancy bits calculation
Example of redundancy bit calculation
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Example of redundancy bit calculation
Error detection using Hamming code
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Error detection using Hamming code
Burst error correction example
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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
VERTICAL REDUNDANCY CHECK (VRC)
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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 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
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
The receiver counts the 1s in each character and comes up
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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LONGITUDINAL REDUNDANCY CHECK
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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
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:
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:
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.
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
Data and redundancy bitsData and redundancy bits
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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
Positions of redundancy bits in Hamming code
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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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