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LECTURE
Error Correction And Detection Method
CHECKSUM
o Error detection method used by the Higher Layers
o Like VRC, LRC, CRC, Checksum is also based on the concept of
redundancy One’s Complement
Finding one’s complement
- Invert every 1 to 0 and 0 to 1
- A and –A are one’s complement of each other
- +A = 1010 -A = 0101
- +0 = 0000 -0 = 1111 Error detection method used by the Higher Layers RC, CRC, Checksum is also based on the concept of redundancy
o The sender subdivides data units into equal segments of ‘n’ bits(16 bits) o These segments are added together using one’s complement o The total (sum) is then complemented and appended to the end of the original data unit as redundancy bits called CHECKSUM o The extended data unit is transmitted across the network o The receiver subdivides data unit as above and adds all segments together and complement the result o If the intended data unit is intact, total value found by adding the data segments and the checksum field should be zero o If the result is not zero, the packet contains an error & the receiver rejects it
Checksum Figure
o o Like VRC, L
CHECKSUM Generator
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Performan o Detects l mber of bits Detects mo n number of bits
xamples
ce of Checksum al errors involving an odd nu o o One pattern remains elusive
st errors involving an eve
E
Example 9.
Suppose a block of 16 bits need to be sent: 10101001 00111001 10101001 00111001
11100010 Sum 00011101 Checksum Sent pattern: 10101001 00111001 00011101 checksum
Example 9. Examples of no error and a burst error
Segment 1 10101001 Segment1 10101111 Segment 2 00111001 Segment2 11111001 e
m om
visible if a bit inversion is balanced by an opposite bit inversion in the corresponding digit of
Segment1 10111101
Ch cksum 00011101 Checksum 00011101
Su 11111111 Sum 11000110 C plement 00000000 Complement 00111001
Error is in another segment
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Hamming Code Each r bit is the VRC bit for one combination of data bits 1(r2) b inary representation includes o on
Summary m
Reading Secti
Section 9.6, 9. A. Forouzan
r it is calculated using all bit positions whose b a 1 in the first(second) position, and s
Checksum Single-Bit Error Correction Ha ming Code
ons
7, “Data Communications and Networking” 4th Edition by Behrouz
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