Error Detection & Error Correction Codes
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This document discusses error detection and correction codes. It defines different types of errors like single bit errors and burst errors. It then explains various error detection methods like vertical redundancy check (VRC), longitudinal redundancy check (LRC), and cyclic redundancy check (CRC) which use redundancy bits to detect errors. The document also covers error correction techniques like Hamming codes which can correct single bit errors using additional redundancy bits in a systematic way based on binary division and polynomial relationships between data and redundancy bits.
![1] Single Bit Error
Single bit errors are the least likely type of errors in serial data transmission because the noise
must have a very short duration which is very rare. However this kind of errors can happen in
parallel transmission.
Fig (b). Single Bit Error
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![2] Burst Error
Fig (c).1 Burst Error
Fig (c).2 Burst Error
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![1] Vertical Redundancy Check (VRC)
Fig (e).1 VRC
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![2] Longitudinal Redundancy Check (LRC)
Fig (e).2 LRC
LCR increases the likelihood of detecting burst errors.
If two bits in one data units are damaged and two bits in exactly the same positions in another
data unit are also damaged, the LRC checker will not detect an error.
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![1] Single bit error correction
To correct an error, the receiver reverses the value of the altered bit. To do so, it must know which
bit is in error.
Number of redundancy bits needed
• Let data bits = m;
• Redundancy bits = r;
Total message sent = m+r;
The value of r must satisfy the following relation:
2r ≥ m+r+1
20](https://image.slidesharecdn.com/160010116021-53-t01-191210093714/85/Error-Detection-Error-Correction-Codes-20-320.jpg)
![2] Hamming Code
Hamming code can be applied to data units of any length and uses the relationship between data
and redundancy bits.For eg.,
21](https://image.slidesharecdn.com/160010116021-53-t01-191210093714/85/Error-Detection-Error-Correction-Codes-21-320.jpg)
Error Detection & Error Correction Codes
- 1. A. D. Patel Institute Of Technology Mobile Computing and Wireless Communication (2170710): A. Y. 2019-20 Error Detection & Error Correction Codes Prepared By : Dhruv V. Shah (160010116053) B.E. (IT) Sem - VII Guided By : Prof. Jayandrath Mangrolia (Dept Of IT , ADIT) Department Of Information Technology A.D. Patel Institute Of Technology (ADIT) New Vallabh Vidyanagar , Anand , Gujarat 1
- 2. Outline Introduction Types Of Error Error Detection Methods of Error Detection Error Correction Hamming Code Example Of Hamming Code 2
- 3. Introduction Networks must be able to transfer data from one device to another with complete accuracy. Data can be corrupted during transmission. For reliable communication, errors must be detected and corrected. Error detection and correction are implemented either at the Data link layer or the Transport layer of the OSI model. 3
- 4. Types Of Error Fig (a). Types Of Error 4
- 5. 1] Single Bit Error Single bit errors are the least likely type of errors in serial data transmission because the noise must have a very short duration which is very rare. However this kind of errors can happen in parallel transmission. Fig (b). Single Bit Error 5
- 6. Example : If data is sent at 1Mbps then each bit lasts only 1/1,000,000 sec. or 1 μs. For a single-bit error to occur, the noise must have a duration of only 1 μs, which is very rare. 6
- 7. 2] Burst Error Fig (c).1 Burst Error Fig (c).2 Burst Error 7
- 8. The term burst error means that two or more bits in the data unit have changed from 1 to 0 or from 0 to 1. Burst errors does not necessarily mean that the errors occur in consecutive bits, the length of the burst is measured from the first corrupted bit to the last corrupted bit. Some bits in between may not have been corrupted. Burst error is most likely to happen in serial transmission since the duration of noise is normally longer than the duration of a bit. The number of bits affected depends on the data rate and duration of noise. Example : If data is sent at rate = 1Kbps then a noise of 1/100 sec can affect 10 bits.(1/100*1000) If same data is sent at rate = 1Mbps then a noise of 1/100 sec can affect 10,000 bits.(1/100*106) 8
- 9. Error Detection Error detection means to decide whether the received data is correct or not without having a copy of the original message. Error detection uses the concept of redundancy, which means adding extra bits for detecting errors at the destination. Fig (d). Redundancy 9
- 10. Methods Of Error Detection Fig (e). Error Detection Methods 10
- 11. 1] Vertical Redundancy Check (VRC) Fig (e).1 VRC 11
- 12. It is also known as parity check. It is least expensive mechanism for error detection. In this technique , the redundant bit called parity bit is appended to every data unit so that the total number of 1s in the unit becomes even (including parity bit). VRC can detect all single – bit errors. It can detect burst errors if the total number of errors in each data unit is odd. VRC can not detect errors where the total number of bits changed is even. 12
- 13. 2] Longitudinal Redundancy Check (LRC) Fig (e).2 LRC LCR increases the likelihood of detecting burst errors. If two bits in one data units are damaged and two bits in exactly the same positions in another data unit are also damaged, the LRC checker will not detect an error. 13
- 14. VRC and LRC : Fig (e).3 VRC & LRC 14
- 15. Cyclic Redundancy Check (CRC) Fig (e).4 CRC 15
- 16. Binary Division: Fig (e).5 Binary Division 16
- 17. Polynomial : Polynomial & Divisor: Standard Polynomial : 17
- 18. The checksum detects all errors involving an odd number of bits. It detects most errors involving an even number of bits. If one or more bits of a segment are damaged and the corresponding bit or bits of opposite value in a second segment are also damaged, the sums of those columns will not change and the receiver will not detect a problem. 18
- 19. Error Correction It can be handled in two ways: 1) Receiver can have the sender retransmit the entire data unit. 2) The receiver can use an error-correcting code, which automatically corrects certain errors. There are two types of Error Correcting techniques : 1) Single bit error correction. 2) Burst error correction. Error Correction can be done with the help of HAMMING CODE. 19
- 20. 1] Single bit error correction To correct an error, the receiver reverses the value of the altered bit. To do so, it must know which bit is in error. Number of redundancy bits needed • Let data bits = m; • Redundancy bits = r; Total message sent = m+r; The value of r must satisfy the following relation: 2r ≥ m+r+1 20
- 21. 2] Hamming Code Hamming code can be applied to data units of any length and uses the relationship between data and redundancy bits.For eg., 21
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