Slide 2:
Types of Errors
Slide 3:
Single-bit error
Slide 4:
Multiple-bit error
Slide 5:
Burst error
Slide 6:
Redundancy
Slide 7:
Error Detection Methods
Slide 8:
VRC
Slide 9:
LRC
Slide 10:
VRC and LRC
Slide 11:
CRC
Slide 12:
Binary Division
Slide 13:
Checksum
Slide 14:
Data Unit and Checksum
Slide 15:
EXAMPLE Sender’s Site
7
11
12
0
6
0
Sum = 36
Wrapped Sum = 6
Checksum = 9 Receiver’s Site
7
11
12
0
6
9
Sum = 45
Wrapped Sum = 15
Checksum = 0 7, 11, 12, 0, 6, 9 Packet 1 0 0 1 0 0 36
1 0
0 1 1 0 6
1 0 0 1 9 1 0 1 1 0 1 45
1 0
1 1 1 1 15
0 0 0 0 0 Details of wrapping and complementing Details of wrapping and complementing
Slide 16:
Error Correction
Slide 17:
Hamming Code Hamming codes can detect up to two simultaneous bit errors, and correct single-bit errors; thus, reliable communication is possible when the Hamming distance between the transmitted and received bit patterns is less than or equal to one.
Slide 18:
Hamming Code
Slide 19:
Hamming Code
Slide 20:
Example of Hamming Code
Slide 21:
Single-bit error
Slide 22:
Error
Detection