computer communication & networks lecture 10 datalink layer: error correction waleed ejaz...
TRANSCRIPT
![Page 1: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/1.jpg)
Computer Communication & Networks
Lecture 10
Datalink Layer: Error Correction
http://web.uettaxila.edu.pk/CMS/coeCCNbsSp09/index.asp
Waleed [email protected]
![Page 2: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/2.jpg)
Data Link Layer
![Page 3: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/3.jpg)
Data Link Layer Topics to CoverError Detection and Correction
Data Link Control and ProtocolsMultiple Access
Local Area Networks
Wireless LANs
![Page 4: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/4.jpg)
Error Correction
1. By retransmission flow and error control protocols
2. Forward Error Correction (FEC) require more redundancy bits should locate the invalid bit or bits n-bit code word contains m data bits + r
redundancy bitsn=m+r
m+r+1 bits discoverable by r bits 2r>=m+r+1
![Page 5: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/5.jpg)
Data and redundancy bitsData and redundancy bits
Number ofdata bits
m
Number of redundancy bits
r
Total bits
m + r
11 2 3
22 3 5
33 3 6
44 3 7
55 4 9
66 4 10
77 4 11
![Page 6: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/6.jpg)
Hamming Code
Hamming codes provide for FEC using a “Block Parity” i.e, instead of one parity bit send a block of parity
bits Allows correction of single bit errors This is accomplished by using more than one
parity bit Each computed on different combination of
bits in the data
![Page 7: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/7.jpg)
Hamming code (Contd.)
![Page 8: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/8.jpg)
Positions of Redundancy Bits
![Page 9: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/9.jpg)
Redundancy Bits Calculation
![Page 10: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/10.jpg)
Example
![Page 11: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/11.jpg)
Error Correction using Hamming Code
![Page 12: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/12.jpg)
Burst Error Correction
![Page 13: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/13.jpg)
Hamming Distance The Hamming distance between two words is
the number of differences between corresponding bits.
Let us find the Hamming distance between two pairs of words.1. The Hamming distance d(000, 011) is 2 because
2. The Hamming distance d(10101, 11110) is 3 because
![Page 14: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/14.jpg)
To guarantee the detection of up to s errors in all cases, the minimum
Hamming distance in a block code must be dmin = s + 1.
Note
![Page 15: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/15.jpg)
Example
![Page 16: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/16.jpg)
To guarantee correction of up to t errors in all cases, the minimum Hamming
distance in a block code must be dmin = 2t + 1.
Note
![Page 17: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/17.jpg)
A code scheme has a Hamming distance dmin = 4. What is the error detection and correction capability of this scheme?
SolutionThis code guarantees the detection of up to three errors(s = 3), but it can correct up to one error. In other words, if this code is used for error correction, part of its capability is wasted. Error correction codes need to have an odd minimum distance (3, 5, 7, . . . ).
Example
![Page 18: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/18.jpg)
Readings
Chapter 10 (B.A Forouzan) Section 10.2,10.5 (Cover only those contents which are related to topics
covered in class)
![Page 19: Computer Communication & Networks Lecture 10 Datalink Layer: Error Correction Waleed Ejaz waleed.ejaz@uettaxila.edu.pk](https://reader035.vdocuments.net/reader035/viewer/2022070413/5697bfec1a28abf838cb88af/html5/thumbnails/19.jpg)