1. Error Detection

2. Error Detection and Correction
Background
Data can be corrupted during transmission
For reliable communication, errors must be detected and corrected
Error detection and correction can be implemented in
Data link layer, or
Transport layer

3. Types of Errors

4. Single-Bit Error Only one bit in the data units has changed Example
sent received

5. Burst Error Two or more bits in the data unit have changed
Errors do not occur in consecutive bits
The length of the burst measured from the first corrupted bit to the last corrupted bit

6. Burst Error Example length of burst error 7 bits
sent
received

7. Detection : Redundancy
1) Two copies of data unit (packet) are sent
Receiving device compares them
Able to detect errors
Transmission time  double
Computational time  slow

8. Detection : Redundancy
2) Only extra information is added
Shorter group of bits may be added to each packet
Used by the receiving device
Discarded when it is used

9. Redundancy Check

10. Redundancy Check Four types of redundancy checks
Vertical redundancy check (VRC)
Longitudinal redundancy check (LRC)
Cyclical redundancy check (CRC)
Checksum

11. Vertical Redundancy Check (VRC)
Implemented in the physical layer
Most common and least expensive mechanism for error detection
Also called parity bit check
A redundant bit, called parity bit, is appended to every data unit
The number of 1s for each data unit, including the parity bit, becomes even
0 is appended when the data unit consists of even 1s

12. VRC

13. VRC Original Data 1110111 1101111 1100100 Parity Bit added
Parity Bit added
Received data
Discard this data

14. VRC
Performance
Detects all single-bit errors (1, 3, 5, .. Bits changed)
Able to detect burst errors if
The total number of bits changed is odd
Cannot detect errors where the total number of bits changed is even

15. Longitudinal Redundancy Check (LRC)
LRC
 Original data + LRC

16. Cyclic Redundancy Check (CRC)
Based on Binary Division

17. CRC Generator
Data plus extra zeros. The number of zeros is one less than the number or bits in the divisor.
When the leftmost bit is zero, we must use 0000 instead of the original divisor

18. CRC Checker A CRC checker functions exactly like the generator
Data + CRC is divided by the predefined divisor
If the remainder is all 0s, accept
Otherwise discard the received data

19. Polynomial
CRC generator (the divisor) is also represented as an algebraic polynomial
It is short
it can be used to prove the concept mathematically

20. Polynomial
Polynomial properties : it should not be divisible by x
it should be divisible by x+1
All burst errors of a length equal to the degree of polynomial are detected

21. Standard polynomial

22. Example of CRC Data = 1010001101 Polynomial = 110101
Calculate: =
Remainder = 1110
Send data frame =
Received Data =
Polynomial =
Calculate: =
Remainder = 0

23. Checksum Used by the higher-layer protocols
Based on concept of redundancy
Consists of checksum generator and checksum checker

24. Checksum Checksum generator
The data unit is divided into k sections, each of n bits
All sections are added together using one’s complement to get the sum
The sum is complemented and becomes the checksum
The checksum is sent with the data

25. checksum Checksum checker
The data unit is divided into k sections, each of n bits
All sections are added together using one’s complement to get the sum
The sum is complemented
If the result is zero, the data are accepted, otherwise, they are rejected

26. Checksum

27. Example : Checksum Generator
(sender)
sum
checksum
 Data sent

28. Example : Checksum Checker
Received data
sum all sections
Sum
Complement  OK

29. Error Correction Two methods Error-correction code
The sender retransmits the entire data
The receiver corrects errors using error-correction code
Error-correction code
More sophisticated than error-detection codes
Require more redundancy bits than error-detection

30. Error Correction (cont.)
Error-correction code (cont.)
The number of bits required to correct multiple-bit or burst error is high
In most case it is inefficient to do
Most error correction is limited to one-, two-, or three-bit errors

31. Error Correction
Self study if you are interested in it.