1. CIS 321 Data Communications & Networking
Chapter 10 – Error Detection and Correction

2. Part 3 - Data Link Layer
Receives services from physical layer and provides services to network layer
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3. Data Link Layer (cont.) Node-to-node delivery Local responsibility
Ensures reliable delivery
Defines frames
Physical addressing
Error control
Flow control
Medium access control
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4. Chapter 10 Error Detection and Correction
Errors are inevitable
Interference
Corruption as a result of transmission
Reliable communication is dependent on being able to detect and correct errors
How will we know an error occurred?
Do we retransmit or correct?
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5. Types of Errors Single-bit error Burst error
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6. Single-bit Errors
Only one bit is changed: 0 changed to 1, or a 1 to a 0
Least likely type of error since noise usually lasts longer than the time to send one bit
More likely in parallel transmission
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7. Burst Errors
Two or more bits in data unit are in error, not necessarily consecutive in order
Most likely in serial transmission
Number of bits affected depend on data rate and noise duration
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8. 10.2 Detection Need to detect before message is processed
Redundancy may be used to add additional bits to a message for error control
Process must be handled by destination
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9. Redundancy University of South Alabama
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10. Detection Methods Parity Check Cyclical Redundancy Check (CRC)
Checksum
Parity and CRC are performed by data link layer; checksum performed by higher-layer protocols
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11. Parity Check Most common and least expensive
In even-parity, a redundant bit (parity bit) is appended to every data unit so total number of 1 bits is even; odd-parity – total should be odd
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12. Even-parity Check University of South Alabama
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13. Example 1
Suppose the sender wants to send the word world. In ASCII the five characters are coded as
The following shows the actual bits sent
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14. Example 2
Now suppose the word world in Example 1 is received by the receiver without being corrupted in transmission.
The receiver counts the 1s in each character and comes up with even numbers (6, 6, 4, 4, 4). The data are accepted.
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15. Example 3
Now suppose the word world in Example 1 is corrupted during transmission.
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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16. Simple Parity Performance
Can detect all single-bit errors
May detect all burst errors as long as total number of bits changed is odd
Cannot detect errors when total number of bits changed is even since parity check will pass even though errors had occurred
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17. Two-Dimensional Parity Check
Data unit is divided into rows and columns; parity checks are performed on corresponding bits of each column
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18. Two-Dimensional Parity
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19. Two-Dimensional Parity Performance
Increases likelihood of detecting burst errors
LRC of n bits can easily detect a burst error of n bits
May also detect many burst errors of more than in n bits
Cannot detect errors when two bits in one data unit are damaged and two bits in exactly the same positions in another data unit are damaged
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20. Cyclic Redundancy Check (CRC)
Parity checks based on addition; CRC based on binary division
A sequence of redundant bits (a CRC or CRC remainder) is appended to the end of the data unit
These bits are later used in calculations to detect whether or not an error had occurred
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21. CRC Steps
On sender’s end, data unit is divided by a predetermined divisor; remainder is the CRC
When appended to the data unit, it should be exactly divisible by a second predetermined binary number
At receiver’s end, data stream is divided by same number
If no remainder, data unit is assumed to be error-free
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22. Deriving the CRC
A string of 0s is appended to the data unit; n is one less than number of bits in predetermined divisor
New data unit is divided by the divisor using binary division; remainder is CRC
CRC of n bits replaces appended 0s at end of data unit
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23. CRC Generator and Checker
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24. CRC Generator Uses modulo-2 division Resulting remainder is the CRC
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25. CRC Checker Performed by receiver Data is appended with CRC
Same modulo-2 division
If remainder is 0, data are accepted
Otherwise, an error has occurred
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26. Polynomials Used to represent CRC generator
Cost effective method for performing calculations quickly
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27. Standard Polynomials Name Polynomial Application CRC-8 x8 + x2 + x + 1
ATM header
CRC-10
x10 + x9 + x5 + x4 + x 2 + 1
ATM AAL
ITU-16
x16 + x12 + x5 + 1
HDLC
ITU-32
x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x + 1
LANs
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28. CRC Performance
Can detect all burst errors affecting an odd number of bits
Can detect all burst errors of length less than or equal to degree of polynomial
Can detect with high probability burst errors of length greater than degree of the polynomial
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29. Checksum Performed by higher-layer protocols
Also based on concept of redundancy
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30. Checksum Generator
At sender, checksum generator subdivides data unit into k equal segments of n bits
Segments are added together using one’s complement arithmetic to get the sum
Sum is complemented and becomes the checksum, appended to the end of the data
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31. Checksum
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32. Checksum Checker Receiver subdivides data unit in k sections of n bits
Sections are added together using one’s complement to get the sum
Sum is complemented
If result is zero, data are accepted; otherwise, rejected
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33. Performance
Detects all errors involving odd number of bits, most errors involving even number of bits
Since checksum retains all carries, errors affecting an even number of bits would still change the value of the next higher column and the error would be detected
If a bit inversion is balanced by an opposite bit inversion, the error is invisible
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34. 10.3 Error Correction
Requires more redundancy bits; must know not only that an error had occurred, but where the error occurred in order to correct it
Correction simply involves flipping the bit
Hamming code may be applied to identify location where error occurred by strategically placed redundancy bits
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35. Redundancy Bits University of South Alabama
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36. Example Hamming Code For a seven-bit data sequence
r1: bits 1, 3, 5, 7, 9, 11
r2: bits 2, 3, 6, 7, 10, 11
r3: bits 4, 5, 6, 7
r4: bits 8, 9, 10, 11
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37. Example Hamming Code University of South Alabama
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38. Error Detection using Hamming Code
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39. Burst Error Correction
By rearranging the order of bit transmission of the data units, the Hamming code can correct burst errors
Organize N units in a column and send first bit of each, followed by second bit of each, and so on
Hamming scheme then allows us to correct corrupted bit in each unit
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40. Burst Error Correction Example
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41. Coming Up… Chapter 11 Data Link Control and Protocols Flow Control
Error Control
Protocols
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42. Credits
All figures obtained from publisher-provided instructor downloads
Data Communications and Networking, 3rd edition by Behrouz A. Forouzan.  McGraw Hill Publishing, 2004
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