EC-356 Data Link Layer

7/31/2019 EC-356 Data Link Layer

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Error Control

Feedback: Using special control frames. To ensure reliable delivery

is to provide the sender with some feedback.

Sender

Data Frame

ReceiverAcknowledgement (ACK)

Or negative Acknowledgement (NAK)

Timers : Hardware troubles may cause special control frames tovanish completely and the receiver will not react at all.

Sequence Numbers : To outgoing frames, to prevent receiver from

accepting the same frame two or more times, and pass it to thenetwork layer more than once.

To help receiver distinguish retransmissions from originals.


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EDC= Error Detection and Correction bits (redundancy)D = Data protected by error checking, may include header fields

Error detection not 100% reliable! protocol may miss some errors, but rarely larger EDC field yields better detection and correction


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Isolated Errors : every packet would be in error

Advantage:

Transmission errors : generated by physical processes, errors

on some media tend to come inbursts rather than singly.

Disadvantage: They are much harder to detect and correct than

isolated errors.

bursty error: only one packet is incorrect


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Error-Correcting Codes

m data bits rcheck bits

What is a codeword ?

n=m+r

There are 2npossible codewords and 2mpossible data messages.

Hamming distancebetween codewords:

min d(C1,C2)=number of (same bit position) bits which differ

d(10010010,00010001)=3

If two codewords are a hamming distance dapart, it will require d

single-bit errors to convert one into the other.


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In most data transmission applications, all 2m

possible datamessages are legal, but due to the way the check bits are

computed, not all 2npossible codewords are used.

Given the algorithm for computing the check bits, it ispossible to construct a complete list of codewords, and from

this list find the two codewords whose Hamming distance is

minimum. This distance is the Hamming distance of the

complete code.


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To detect derrors, you need a distance d+1 code.

d+1

radius=dbits

distance


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To correct derrors, you need a distance 2d+1 code.


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Parity check is a code with distance 2. Therefore, it can detect

single-bit error.

Consider a code with only 4 valid codewords:0000000000, 0000011111, 1111100000, 1111111111

,

bit errors and correct double errors.

If the codeword 0000000111 arrives and we know at most two

bits are in error, the receiver knows that the original must havebeen 0000011111. If, however, a triple error changes

0000000000 into 0000000111, the error will not be corrected

properly.


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A 1-bit error correcting code (Hamming code)

m data bits rcheck bits

n=m+r

distance 1 from it.

Thus each of the 2m legal messages requires n+1 bit patterns

dedicated to it.

r

rmm

nm

rm

rm

n

2)1(

22)1(

22)1(

++

++

++

Therefore,


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Single Bit Parity:Detect single bit errors

Two Dimensional Bit Parity:Detect and correctsingle bit errors

0 0


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There is a lower limit on the number of check bits needed to

correct single errors.

In practice, it can be achieved using a method due to Hamming.

The bits of codewords are numbered consecutively, starting with

bit 1 at the left end. The bits that are power of 2 (1, 2, 4, 8, )

r h k i

The rest are filled up with the data bits. Each check bit forces

the parity of some collection of bits, including itself, to be even

(or odd).


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Error-Correcting Codes

A 1-bit error

correcting code

(Hamming code)

Correct 12-bit burst

errors by transmitting

vertically.


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Error-detecting Codes

error control: error detection or error correction?

assume error rate=1/106 data=1000 bits

error detecting check bits: 1 bit (e.g. parity check)

. .

In 103packets:

error detecting overhead=103+1001=2001 bits

error correcting overhead=10*103bits=10000 bits

retransmission


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The Data Link Layer

Error-detecting Codes

CRC (Cyclic Redundancy Code)

Treat bit strings as polynomials with coefficient 0 and 1.

(E.g. 10001001:x7+x3+1, 01010111=x6+x4+x2+x+1)

. .

(the generating polynomial, G(x))2.

Assume with remainder

Then transmit

M x x

G xA x R x

T x M x x R x

r

r

( )

( )( ) ( ).

( ) ( ) ( ).

=

=

3. When receiver receives T(x), it divides it by G(x). If there

is a remainder, then an error has occurred.

(All the above operations are done in modulo 2.)


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Elementary Data Link Protocols


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1. An Unrestricted Simplex Protocol


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2. A Simplex Stop-and-Wait Protocol


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3. A Simplex Protocol for Noisy Channel

sequence numbers (to number packets and ACKs)

senderP(1) P(2)

senderP(1) P(1)

time-out

receiverACK

receiverACK

error

If there is no sequence number for packets, the receiver

can not distinguish between these two cases.

new old


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The sender cannot tell whether this

ACK is for P(1) or P(2) if not

um ered.

A potential failure

ACKs must also be numbered.

sender

receiver

P(1) P(1) P(2)

error

ACK ACK

time-out


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3. A Simplex Protocol for Noisy Channel


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EC-356 Data Link Layer

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