1. Lecture 12 Layer 2 – Data Link Layer Protocols
CS 453 Computer Networks
Lecture 12
Layer 2 – Data Link Layer
Protocols

2. Error Detection There are two forms of error control
Error Correction
Both involve adding extra bits to the communication stream
Error detection - sensing and handling errors – resend, drop, …
Error correction – sensing and correcting errors with available information

3. Error Detection Think about this –
What is the simplest way to detect errors in transmitted frames?
Send each frame twice
Compare, if different – probable error
Is this efficient?
Why?
Is it fool-proof?
What kind of errors could slip by?

4. Error Detection You’re right (I hope) It is not efficient
It reduces effective data rate in half
Repetitive errors to the same bit sequences would slip through
Consistently dropping the first five bits

5. Error Detection Parity bits Simple form of error detection
Even or odd parity
For 7 bits add an 8th bit such that the number of 1 bits is an even number (even parity)..
…or odd (odd parity)
If parity is even and the receiver gets a byte with an odd number of 1s, then error 1 1 1 1
Parity bit
Data bits

6. Error Detection Parity bits Very efficient – adds one bit per 7 bits
Not very powerful – can detect 1 bit errors

7. Error Detection Two Dimensional Parity Imagine data stream as matrix
6 byte data stream
Add parity bit per byte (simple parity)
Add a parity byte where each bit is a parity bit for that bit position across the bytes in the frame
From Peterson & Davie (2003) pg. 90

8. Error Detection Two Dimensional Parity Fairly efficient
Add 14 bits of redundant information to a 42 bit data stream
Fairly powerful
Can detect all 1, 2 and 3 bit errors
Can detect some 4 bit errors
Why can it detech multibit errors
Can 2D parity be used to correct errors?

9. Error Detection Internet Checksum Add the words in a data stream
Suppose you have a stream of 16 bit integers
Add them using ones complement arithmetic
Sender calculates checksum
…then sends data stream+checksum
Receiver receives data stream+checksum
Receive calculates new checksum on received data stream
Compares it to the received checksum
If match – probably no error
If no match – probably error

10. Error Detection Internet Checksum Very efficient Fairly weak
Only a few bits for a very long data stream
Fairly weak
For example, a dropped bit in one word and a spuriously added bit in another word would not be detected - would result in same ckecksum
Easy to implement in hardware or software

11. Error Detection CRC – Cyclic Redundancy Check
More generally knows an polynomial code
CRC data stream…
d bits
r bits
D: data bit from sender
R: CRC bit

12. Error Detection CRC – Cyclic Redundancy Check
Sender and Receiver must agree on a r+1 bit pattern – referred to as G
Some things to consider
CRC calculations are done with base 2 arithmetic
addition/subtraction done with XOR
multiplication/division done with left/right register shifts

13. Error Detection CRC – Cyclic Redundancy Check What to use for R
D * 2r XOR R = nG
says that D * 2r XOR R is an even multiple of G
…or divisible with no remainder
If we XOR R to both sides of above
D * 2r = nG XOR R
If we divide D * 2r by G the remainder is R
R = remainder(D * 2r /G)
Based on Kurose & Ross, Computer Networking: a top down structured approach using the Internet (2005) pg. 428

14. from: Peterson & Davie (2003) pg.95
Error Detection
CRC – Cyclic Redundancy Check
consider – original message D
D =
left shift 3 bit positions (multiply)
Divide by G
Remainder = R
for CRC check
if R is subtracted from D…
D-R is evenly divisible by G
If receiver gets D,R where (D-R ) /G has remainder there is an error
from: Peterson & Davie (2003) pg.95

15. Error Detection CRC – Cyclic Redundancy Check CRC is very powerful
Can detect multibit errors
Can detect burst errors < r+1 bits
So where does G come from?
Mathematics
There are lots of codes, predetermined
For example-
CRC
IEEE