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Behrouz A. Forouzan Data communication and NetworkingDr. Gihan NAGUIB1

Data Link LayerData Link Layer

P RT IIIRT III

Behrouz A. Forouzan Data communication and NetworkingDr. Gihan NAGUIB 2

Data link layer duties


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Chapters

Chapter 10Error Detection and Correction

Chapter 11 Data Link Control and Protocols

Chapter 12Multiple Access

Chapter 13Wired LANs: Ethernet

Chapter 15Connecting LANs, Backbone networks

and virtual LANs


Chapter 10

Error Detection

and

Correction


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Network must be able to transfer data from

one device to another with acceptable

accuracy.

Data can be corrupted during transmission.

For reliable communication, errors must be

detected and corrected.

NoteNote::


Types of ErrorTypes of Error

Single-Bit Error

Burst Error


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Single-bit error

In a single-bit error, only one bit in the data

unit has changed. (0 1 or 1 0)

Does the Single-bit error happen in parallel or

serial transmission ? Why ?

Single-bit error most likely to occur in parallel

transmission(eg. between CPU and memory)

STX (Start of text)LF (Line feed)


Burst error

A burst error means that 2 or more bits in the data unit have changed

Burst error does not necessarily mean that the errors occur in consecutive

bits

Most likely to happen in a serial transmission

Number of bits affected depends on the data rate and noise duration

If the data is sent at 1 kbps, a noise of 1/100 s can affect 10 bits.

If the data is sent at 1 Mbps, a noise of 1/100 s can affect 10000 bits.


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ERROR DETECTION

Error detection uses the concept of redundancy, whichmeans adding extra bitsfor detecting errors at thedestination.


ERROR DETECTION

Error can be detected by using block coding:

Dived the message into blocks, each of k bits, called datawords.

Add r redundant bits to each block to make the length

n = k + r.

The resulting n bits blocks are called codewords

Pages 274 until the end of section 10.2 are excluded.


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Error Detection methods


1.Parity Check

The most common and least expensive

Simple or Two Dimensional

1.1 simple parity check

a parity bit (extra bit) is

added to every data

unit so that the total

number of 1s is even or

odd (for odd-parity).


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1.Parity Check

1.1 simple parity check


ExampleExample 11

Suppose the sender wants to send the word world. In ASCII

the five characters are coded as

1110111 1101111 1110010 1101100 1100100

The following shows the actual bits sent

11101110 11011110 11100100 11011000 11001001

w O r l d


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ExampleExample 22

Now suppose the word world in Example 1 is received by

the receiver without being corrupted in transmission.

11101110 11011110 11100100 11011000

11001001

The receiver counts the 1s in each character and comes up

with even numbers:

(6, 6, 4, 4, 4). The data are accepted.


ExampleExample 33

Now suppose the word world in Example 1 is corrupted

during transmission.

11111110 11011110 11101100 11011000 11001001

The receiver counts the 1s in each character and comes up

with even and odd numbers:

(7, 6, 5, 4, 4).

The receiver knows that the data are corrupted, discards

them, and asks for retransmission.


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Performance of Simple Parity Check

Example:

We have an even-parity data unit where the total number of 1s, includingthe parity bit, is 6: 1000111011.

If any 3 bits changed, the resulting parity will be odd and the error

will be detected:

1111111011: 9 ones

0110111011: 7 ones

1100010011: 5 ones

The same holds true for any odd number of errorsSuppose 2 bits are changed:

1110111011: 8 ones

1100011011: 6 ones

The number of 1s in the data unit is still evenThe same holds true for any even number of errors

The parity checker cannot detect errors when number of bits changed

is even. The change cancel each other and the data unit will pass a

parity check even though the data unit is damaged.


Simple parity check can detect allSimple parity check can detect all

singlesingle--bit errorsbit errors. It can detect. It can detect burstburst

errors only if the total number oferrors only if the total number of

errors in each data unit iserrors in each data unit is odd.odd.

NoteNote::


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1.2 Two-dimensional parityCalculate the parity bit for each data unit, then organize them into table (rows

and columns)

Calculate the parity bit for each column and create a new row (column parity)

A redundant row of bits is added to the whole block.


In two-dimensional parity check, a

block of bits is divided into rows and

a redundant row of bits is added to

the whole block.

NoteNote::


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ExampleExample 44

Suppose the following block is sent:

10101001 00111001 11011101 11100111 10101010

However, it is hit by a burst noise of length 8, and some

bits are corrupted.

10100011 10001001 11011101 11100111 10101010

When the receiver checks the parity bits, some of the bits

do not follow the even-parity rule and the whole block isdiscarded.( see next slide)


ExampleExample 44

At Sender: At receiver:

Error in colum positions: 2, 4, 5 ,6 and 8

1 0 1 0 1 0 0

0 0 1 1 1 0 0

1 1 0 1 1 1 0

1 1 1 0 0 1 1

1

1

1

1

1 0 1 0 1 0 1 0

1 0 1 0 00 1

10 0 01 0 01 1 0 1 1 1 0

1 1 1 0 0 1 1

1

11

1

1 0 1 0 1 0 1 0

1 0 1 1 1 0 1 0


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Behrouz A. Forouzan Data communication and Networking23

Two-dimensional Performance

Increases the likelihood of detecting burst errors.

A redundancy of n-bits can detect a burst error of n bits

A burst error of more than n bits is also detected with a

very high probability

One pattern of errors still elusive:

If 2 bits in one data unit are damaged and two bits in

exactly the same position in anther data unite are also

damaged. The error will not be detected.

Dr. Gihan NAGUIB

Behrouz A. Forouzan Data communication and Networking 24

Two-dimensional Performance

Dr. Gihan NAGUIB


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2. Cyclic Redundancy Check CRC

Uses Module-2 Binary division


Cyclic Redundancy Check CRC

In CRC generator (At sender)A string of n 0s is appended to the data unit

The number n is 1 less than the number of bits in the divisor

Divide the data word plus appended zeros by the divisor

Use module-2 binary division:

oThere is no carry when you add or subtract two digits in a

column

oAddition and subtraction gives the same results

o This means: you can use XOR operation for both Addition

and subtraction

The remainder resulting from the division is the CRC

The CRC of n bits replaces the appended 0sat the end of the data

unit.

Appending CRC to the end of the data must make resulting bit

sequence divisible by the divisor


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Binary division in a CRC generator

The leading zero of the

remainder is dropped


Cyclic Redundancy Check CRC

In CRC Checker (At receiver):

After receiving the data appended with the

CRC, it does the same module -2 division

If the remainder is all 0sthe CRC dropped and

the data are accepted ( the data is correct)

If the remainder is not equal zero, the received

stream of bits is discarded and data must be resent

( the data is corrupted)


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Binary division in CRC checker


Example


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Example: Division in the CRC decoder for two cases


A polynomial

The divisor in CRC generator is most often represented

not as string of 1s and 0s, but as an algebraic polynomial.

The polynomial is used for two reasons: it is Short and

Can be used to prove the concept mathematically

A polynomial should be selected to have the following :

1. It should not be divisible by x.( i.e the coefficient ofterm X0should be 1)

2. It should be divisible by x+1.The first condition: guarantees that all the burst errors of a

length equal to the degree of the polynomial are detected.

The Second condition: guarantees that all the burst errors

affecting an odd number of bits are detected.


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A polynomial representing a divisor

Note that:

the degree of a polynomial is 1 less that the number of bits in the pattern.

The bit pattern in this case has 7 bit


A polynomial representing a divisor


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ExampleExample 55

We cannot choose:

X (binary 10) or

X2+ X(binary 110) becauseboth are divisible by x.

We can choose

X + 1(binary 11) because it is not divisible by x, but is divisible

byx + 1.

X2+ 1(binary 101) becauseit is divisible by x + 1 (binary

division).


Standard polynomialsStandard polynomials

Name Polynomial Application

CRCCRC--88 x8 +x2 +x+1 ATM header

CRCCRC--1010 x10+x9 +x5 +x4 +x2+1 ATM AAL

ITUITU--1616 x16+x12+x5 + 1 HDLC

ITUITU--3232x32+x26 +x23+x22+x16+x12+x11+x10

+ x8+x7+x5+x4+x2+x +1LANs


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CRC PerformanceCRC Performance

CRC is very effective error detection method:

1. CRC Can detect all burst errors that affect an odd

number of bits.

2. CRC Can detect all burst errors of length less than

or equal to the degree of the polynomial

3. CRC can detect, with very high probability, bursterrors of length greater than the degree of the

polynomial.


ExampleExample 66

The CRC-12

x12+ x11+ x3+ x + 1

which has a degree of 12, will detect1. all burst errors affecting an odd number of bits,

2. will detect all burst errors with a length less

than or equal to 12, and

3. will detect, 99.97 percent of the time, burst

errors with a length of 12 or more.


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3. Checksum

Like parity checks and CRC, the checksum based on redundancy

The checksum is used in the Internet by several protocols notThe checksum is used in the Internet by several protocols not

at the data link layer (Checksum used for example in networkat the data link layer (Checksum used for example in network

layer ).layer ).


Data unit and checksum

The receiver follows these steps:The receiver follows these steps:

1.1. The unit is divided into k sections,The unit is divided into k sections,

each of n bits.each of n bits.

2.2. All sections are added using onesAll sections are added using ones

complement to get the sum.complement to get the sum.

3.3. The sum is complemented.The sum is complemented.

4.4. If the result is zero, the data areIf the result is zero, the data are

accepted: otherwise, rejected.accepted: otherwise, rejected.

The sender follows these steps:The sender follows these steps:

1.1. The unit is divided into k sections,The unit is divided into k sections,

each of n bits.each of n bits.

2.2. All sections are added using onesAll sections are added using ones

complement to get the sum.complement to get the sum.

3.3. The sum isThe sum is complementedcomplementedandand

becomes thebecomes the checksum.checksum.

4.4. The checksum is sent with the data.The checksum is sent with the data.


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ExampleExample 77

Suppose the following block of 16 bits is to be sent using a checksum

of 8 bits.

10101001 00111001

The numbers are added using ones complement

10101001

00111001

------------

Sum 11100010Checksum 00011101

The pattern sent is 10101001 00111001 00011101


ExampleExample 88

Now suppose the receiver receives the pattern sent in Example 7 and

there is no error.

10101001 00111001 00011101

When the receiver adds the three sections, it will get all 1s, which,

after complementing, is all 0s and shows that there is no error.

10101001

00111001

00011101

Sum 1111111 1

Complement 00000000 means that the pattern is OK.


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ExampleExample 99

Now suppose there is a burst error of length 5 that affects 4 bits.

10101111 11111001 00011101

When the receiver adds the three sections, it gets

10101111

11111001

00011101

Partial Sum 111000101

Carry 1

Sum 11000110

Complement 00111001 the pattern is corrupted.


Almost detects all errors involving odd

numbers of bits or even.

if one or more bits of a segment are damaged and

the corresponding bit or bits of opposite value in asecond segment are also damaged,

then the sum of columns will not change. Receiver

will not be able to detect the error

Performance of checksum


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1. Retransmission:

when error is discovered, the receiver can have the

sender retransmit the data unit

2. Forward Error Correction

3. Burst Error Correction

Error Correction


Forward Error Correction

A receiver can use an error-correcting code, which

automatically corrects certain errors.

Error-correcting codes are more sophisticated

than error detection codes and require moreredundancy bits.

Example for a single bit error:

Error Detection: one bit (error or no error)

Error Correction: must know which bit is in

error ( need more than one bit).


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ExampleTo correct a single-bit error in an ASCII character (7-bit), the

error correction must distinguish between: no error, error

in position1 .,error in position 7( 8 states)

It require more redundancy bits to show the 8

states

3-bit redundancy code: can indicate the location of 8

different possibilities.

But can not know if an error occur in theredundancy bits. Additional bits are required to

cover all possible error location( including

redundancy bits)



The number of redundancy bits rto correct agiven number of data bitsm is :

2r >= m + r + 1

2r = number of states m + r indicates the location of an error in

each m + r positions

1 indicates no error

The value of r can be determined by plugging in

the value of m

Eg. m=7 , the smallest r that can satisfy this is 4


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Data and redundancy bitsData and redundancy bits

Number of

data bits

m

Number of

redundancy bits

r

Total

bits

m + r

11 2 3

22 3 5

33 3 6

44 3 7

55 4 9

66 4 10

77 4 11

2r > = m + r + 1


Hamming code

Create the code word as follows:

Mark all bit positions that are powers of two as parity bits. (positions 1,

2, 4, 8, 16, 32, 64, etc.)

All other bit positions are for the data to be encoded. (positions 3, 5, 6,

7, 9, 10, 11, 12, 13, 14, 15, 17, etc.)

The key to the Hamming Code is the use of extra parity bits to

allow the identification of a single error

Positions of redundancy bits:


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Redundancy bit Calculation

Binary(data) Decimal no

00113

01015

01106

01117

10019

101010

101111

Data ward =7 bits , r =4

Codeward =7+4=11

Bit r1: bits 3, 5, 7, 9,11

Bit r2: bits 3,6,7,10,11

Bit r4: 5,6,7

Bit r8: 9, 10,11



Each parity bit calculates the even parity for someof the bits in thecode word. The position of the parity bit determines the sequence of

bits that it alternately checks and skips.

Position 1( r1):check 1 bit, skip 1 bit, check 1 bit, skip 1 bit, etc.

(1,3, 5, 7, 9, 11, 13, 15,...)Position 2 (r2):check 2 bits, skip 2 bits, check 2 bits, skip 2 bits, etc.

(2, 3, 6, 7, 10, 11, 14, 15,...)Position 4 (r4):check 4 bits, skip 4 bits, etc

(4, 5, 6, 7, 12, 13, 14, 15,...)

Position 8(r8):check 8 bits, skip 8 bits, etc.

(8-15, 24-31, 40-47,...)Set a parity bit to 1if the total number of ones in the positions it

checks isodd. Set a parity bit to 0if the total number of ones in the

positions it checks is even.



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Redundancy bits calculation


Example of redundancy bit calculation

Using even parity


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Error detection and correction using Hamming code


Burst error correction

Hamming code cannot correct a burst error

directly, it is possible to rearrange the data and

then apply the code.

Organize Nunits in a column and then send thefirst bit for each, followed by the second bit of

each , and so on.

If a burst error of Mbits occurs (M


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Burst error correction example

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