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**Lecture 12 Layer 2 – Data Link Layer Protocols**

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

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**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

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**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?

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**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

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**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

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**Error Detection Parity bits Very efficient – adds one bit per 7 bits**

Not very powerful – can detect 1 bit errors

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**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

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**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?

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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