CS 453CS 453Computer NetworksComputer Networks

Lecture 12Lecture 12

Layer 2 – Data Link LayerLayer 2 – Data Link Layer

ProtocolsProtocols

Error Detection

There are two forms of error control Error Detection Error Correction

Both involve adding extra bits to the communication streamError detection - sensing and handling errors – resend, drop, …Error correction – sensing and correcting errors with available information

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?

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

Error DetectionParity 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 0 1 0 0 1 0 1

Parity bitData bits

Error DetectionParity bits Very efficient – adds one bit per 7 bits Not very powerful – can detect 1 bit errors

Error DetectionTwo 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

1011110 1

1101001 0

0101001 1

1011111 0

0110100 1

0001110 1

1111011 0

Paritybits

Paritybyte

Data

From Peterson & Davie (2003) pg. 90

Error DetectionTwo Dimensional Parity Fairly efficient

Add 14 bits of redundant information to a 42 bit data stream

Fairly powerfulCan 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?

Error DetectionInternet Checksum

Add the words in a data streamSuppose 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

Error DetectionInternet Checksum Very efficient

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

Error DetectionCRC – Cyclic Redundancy Check

More generally knows an polynomial code

CRC data stream…

D: data bit from sender R: CRC bit

d bits r bits

Error DetectionCRC – 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

arithmeticaddition/subtraction done with XOR

multiplication/division done with left/right register shifts

Error DetectionCRC – 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

Error DetectionCRC – Cyclic Redundancy Check

consider – original message D

D = 10011010left 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

Generator 11011111100110011010000 Message1101

10011101

10001101

10111101

11001101

10001101101 Remainder

Error DetectionCRC – Cyclic Redundancy CheckCRC 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-32 10000010011000010001110110110111 IEEE