error dection and corection

8/7/2019 error dection and corection

1/41

Error Detection

and Correction

Types of Errors

Detection Correction


2/41

Basic conceptsBasic concepts

Networks must be able to transfer data from onedevice to another with complete accuracy.

Data can be corrupted during transmission.

For reliable communication, errors must bedetected and corrected.

Error detection and correction are

implemented either at the data link layeror the transport layer of the OSI model.


3/41

Types of Errors


4/41

Single-bit error


5/41

Single bit errors are the least likely type oferrors in serial data transmission because the

noise must have a very short duration which isvery rare. However this kind of errors canhappen in parallel transmission.

Example:Example:

If data is sent at 1Mbps then each bit lasts only1/1,000,000 sec. or 1 s.

For a single-bit error to occur, the noise musthave a duration of only 1 s, which is very rare.


6/41

Burst error


7/41


8/41

The term burst errorburst error means that two or

more bits in the data unit have changed

from 1 to 0 or from 0 to 1.

Burst errorsdoes notnecessarilymean that

the errors occur in consecutive bits, the

length of the burst is measured from the

first corrupted bit to the last corrupted bit.

Some bits in between may not have beencorrupted.


9/41

Burst error is most likely to happen in serial

transmission since the duration of noise is normally longer

than the duration of a bit.The number of bits affected depends on the data rate and

duration of noise.

Example:Example:

If data is sent at rate = 1Kbps then a noise of 1/100 sec can affect

10 bits.(1/100*1000)

If same data is sent at rate = 1Mbps then a noise of 1/100 sec can

affect 10,000 bits.(1/100*106)


10/41

Error detectionError detection

Error detection means to decide whether the

received data is correct or not without having a

copy of the original message.

Error detection uses the concept of redundancy,

which means adding extra bits for detectingerrors at the destination.


11/41

Error detection uses the concept of

redundancy, which means adding extra

bits for detecting errors at the

destination.


12/41

Redundancy


13/41

Four types of redundancy checks are usedFour types of redundancy checks are used

in data communicationsin data communications


14/41

Vertical Redundancy Check

VRC


15/41

PerformancePerformance

It can detect single bit error

It can detect burst errors only if the total

number of errors is odd.


16/41

Longitudinal Redundancy Check

LRC


17/41


LCR increases the likelihood of detectingburst errors.

If two bits in one data units are damaged

and two bits in exactly the same positions inanother data unit are also damaged, the

LRC checker will not detect an error.


18/41

VRC and LRC


19/41

Cyclic Redundancy Check

CRC


20/41

Cyclic Redundancy CheckCyclic Redundancy Check

Given a k-bit frame or message, thetransmitter generates an n-bit sequence,known as a frame check sequence(FCS), so

that the resulting frame, consisting of (k+n)bits, is exactly divisible by somepredetermined number.

The receiver then divides the incomingframe by the same number and, if there isno remainder, assumes that there was noerror.


21/41

Properties of polynomial

It is obvious that we cannot choose x (binary 10) or x2

+ x (binary 110) as the polynomial because both aredivisible by x. However, we can choose x + 1 (binary

11) because it is not divisible by x, but is divisible by x

+ 1. We can also choose x2 + 1 (binary 101) because it

is divisible by x + 1 (binary division).


22/41

Binary division in a CRC generator


23/41

Binary division in CRC checker


24/41

Polynomial


25/41

Polynomial and Divisor


26/41

Standard Polynomials


27/41

Checksum


28/41

At the senderAt the sender

The unit is divided into ksections, each ofn

bits.

All sections are added together using onescomplement to get the sum.

The sum is complemented and becomes the

checksum.

The checksum is sent with the data


29/41

At the receiverAt the receiver

The unit is divided into ksections, each ofn

bits.

All sections are added together using onescomplement to get the sum.

The sum is complemented.

If the result is zero, the data are accepted:otherwise, they are rejected.


30/41


The checksum detects all errors involving an oddnumber of bits.

It detects most errors involving an even number of

bits.If one or more bits of a segment are damaged and the

corresponding bit or bits of opposite value in a second

segment are also damaged, the sums of those columns

will not change and the receiver will not detect aproblem.


31/41

Suppose the following block of 16 bits is to be sent using achecksum of 8 bits.

10101001 00111001

The numbers are added using ones complement10101001

00111001

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

Sum 11100010

Checksum 00011101

The pattern sent is 10101001 0011100100011101


32/41

Now suppose the receiver receives the pattern sent in 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 11111111

Complement 00000000 means that the pattern is

OK.


33/41

Error CorrectionError Correction

It can be handled in two ways:

1) receiver can have the sender retransmit the

entire data unit.

2) The receiver can use an error-correcting

code, which automatically corrects certain

errors.


34/41

CorrectionCorrection

Retransmission

Forward Error Correction

Burst Error Correction


35/41

Single-bit error correctionSingle-bit error correctionTo correct an error, the receiver reverses the valueof the altered bit. To do so, it must know which bit

is in error.

Number of redundancy bits needed

Let data bits = m

Redundancy bits = r

Total message sent = m+r

The value of r must satisfy the following relation:

22rr m+r+1 m+r+1


36/41

Data and redundancy bitsData and redundancy bits

Number ofdata bits

m

Number ofredundancy bits

r

Totalbits

m + r

11 2 3

22 3 5

33 3 6

44 3 7

55 4 9

66 4 10

77 4 11

P iti f d d bit i H i


37/41

Positions of redundancy bits in Hamming

code

R d d bit l l ti


38/41

Redundancy bits calculation

Example of redundancy bit calculation


39/41

Example of redundancy bit calculation

Error detection using Hamming code


40/41

Error detection using Hamming code

Burst error correction example


41/41

Burst error correction example

error dection and corection

Documents