1. Protocols and the TCP/IP Suite
Lecture 4
Error Detection
Forward Error Correction (Hamming Code)
Chapter 2

2. Protocols and the TCP/IP Suite
1- Error Detection
1.1 Parity check
1.2 Two dimensional parity check
1.3 Checksum
1.4 Cyclic redundancy check
Chapter 2

3. Protocols and the TCP/IP Suite
1.1 Parity check
- Appends a parity bit to the end of the data.
Even
Odd
- It can detect all single bit errors.
It can also detect burst errors, if the number of
bits in error is odd.
Chapter 2

4. 1.2 Two Dimensional Parity Check
Protocols and the TCP/IP Suite
1.2 Two Dimensional Parity Check
Parity check bits are calculated for each row, which is
equivalent to a simple parity check bit.
Parity check bits are also calculated for all columns.
Both are sent along with the data.
Chapter 2

5. 1.2 Two Dimensional Parity Check
Protocols and the TCP/IP Suite
1.2 Two Dimensional Parity Check
Chapter 2

6. Protocols and the TCP/IP Suite
1.3 Checksum
- At the sender’s end, the data is divided into segments.
The segments are added using ones complement arithmetic to get the sum.
The sum is complemented to get the checksum which is sent along with the data segments.
At the receiver, the received segments are added using ones complement arithmetic to get the sum.
If the complement of the sum is zero, the received data is accepted.
Chapter 2

7. Protocols and the TCP/IP Suite
1.3 Checksum
Ex: Find the checksum at the sender and receiver for the following sequence:
__________ 1
_______________
______________
_____________
________________
Sum:
Checksum:
__________ 1
_______________
______________
_____________
sum:
Checksum:
Chapter 2

8. 1.4 Cyclic Redundancy Check
Protocols and the TCP/IP Suite
1.4 Cyclic Redundancy Check
The sender generates a bit sequence known as a frame check sequence (FCS), so that the resulting frame consisting of the original data followed by this FCS. - FCS is the remainder which obtained from dividing the original data M(X) by generator polynomial G(x). - The receiver divides the incoming frame by G(X), if there is no remainder the received data has no errors.
Chapter 2

9. 1.4 Cyclic Redundancy Check
Protocols and the TCP/IP Suite
1.4 Cyclic Redundancy Check
________
_________
__________
0 0 0
1011
1001
________
_________
__________
FCS
1011
1001
Chapter 2

10. 1.4 Cyclic Redundancy Check
Protocols and the TCP/IP Suite
1.4 Cyclic Redundancy Check C3 C1 C0 +
000
001
010
101
100
011 1
Initial
FCS
Chapter 2

11. 2- Forward Error Correction
Protocols and the TCP/IP Suite
2- Forward Error Correction
Forward Error correction (FEC) which based on the receiver only is used mainly when retransmissions cannot be requested, e.g., simplex links.
Backward error correction which based on retransmission of the frame when an error is detected is commonly used.
Hamming Code:
It can correct any single bit error
Bits in power of 2 positions (1,2,4,8,) are check bits, the rest are m data bits
Check bit forces the parity of some collection of bit “1” to be even
To see which check bits the data bit in position k contributes to, rewrite k as a sum of powers of 2.
11=1+2+8, 29=
Chapter 2

12. Protocols and the TCP/IP Suite
Hamming Code
EX: If a 12-bit hamming code arrives at receiver, is there any bit error? If so, which bit is wrong?
= =4+1 6=4+2 7= = = = =8+4
Check bit
Checked Data bits
Bits Sequence 1
(Yes) 2
(No) 4
(No) 8
(Yes)
Hence bit 6 = 2+4 is wrong, so correct hamming code should be
Chapter 2