error detection and correction.ppt

8/9/2019 Error detection and correction.ppt

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Error

Detection

And

Correction


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Outline

11 INTRODUCTION INTRODUCTION

2 2 CHECKSUM CHECKSUM


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INTRODUCTION INTRODUCTION

Let us first discuss some issues related, directly

or indirectly, to error detection and correction.


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1. Types of Errors1. Types of Errors

Whenever bits flow from one point to another,they are subject to unpredictable changes because

of interference.

This interference can change the shape of thesignal. The term single-bit error means that only 1

bit of a given data unit (such as a byte, character,

or packet is changed from 1 to ! or from ! to 1!.

The term burst error means that " or more bits

in the data unit have changed from 1 to ! or from

! to 1!.


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Figure : Single-bit and burst error


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2 Redundancy2 Redundancy

The central concept in detecting or correctingerrors is redundancy.

To be able to detect or correct errors, we need to

send some e#tra bits with our data.

These redundant bits are added by the sender

and removed by the receiver.

Their presence allows the receiver to detect or

correct corrupted bits.


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. Detection !ersus Correction . Detection !ersus Correction

T"e correction of errors is more difficult t"an t"e

detection. In error detection, #e are only loo$in% to see if

any error "as occurred. T"e ans#er is a simple yes

or no. &e are not e!en interested in t"e num'er ofcorrupted 'its.

( sin%le)'it error is t"e same for us as a 'urst

error. In error correction, #e need to $no# t"e e*act

num'er of 'its t"at are corrupted and, more

importantly, t"eir location in t"e messa%e.


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+. Codin% +. Codin%

Redundancy is ac"ie!ed t"rou%" !arious codin%

sc"emes.

T"e sender adds redundant 'its t"rou%" a process

t"at creates a relations"ip 'et#een t"e redundant

'its and t"e actual data 'its.

T"e recei!er c"ec$s t"e relations"ips 'et#een t"e

t#o sets of 'its to detect errors.

T"e ratio of redundant 'its to data 'its and t"e

ro'ustness of t"e process are important factors in

any codin% sc"eme.


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2.CHECKSUM 2.CHECKSUM

C"ec$sum is an error)detectin% tec"niue

t"at can 'e applied to a messa%e of any len%t".

In t"e Internet, t"e c"ec$sum tec"niue is

mostly used at t"e net#or$ and transport layer

rat"er t"an t"e data)lin$ layer.


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Figure: Checksum


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Concept Concept

T"e idea of t"e traditional c"ec$sum is simple. &es"o# t"is usin% a simple e*ample.


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Suppose the message is a list of five 4-bit numbers that we

want to send to a destination. In addition to sending these

numbers, we send the sum of the numbers. For example, if

the set of numbers is (7, 11, 1, !, "#, we send (7, 11, 1, !,

", $%#, where $% is the sum of the original numbers. $he

re%eiver adds the five numbers and %ompares the result withthe sum. If the two are the same, the re%eiver assumes no

error, a%%epts the five numbers, and dis%ards the sum.

&therwise, there is an error somewhere and the message not

a%%epted.

Example 1


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In the previous example, the de%imal number '" in binar is

(1!!1!!#. $o %hange it to a 4-bit number we add the extra

leftmost bit to the right four bits as shown below.

Example 2

Instead of sending '" as the sum, we %an send " as the sum

(7, 11, 1, !, ", "#. $he re%eiver %an add the first five

numbers in one)s %omplement arithmeti%. If the result is ",the numbers are a%%epted* otherwise, the are re+e%ted.


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et us use the idea of the %he%sum in xample . $he

sender adds all five numbers in one)s %omplement to get the

sum / ". $he sender then %omplements the result to get the

%he%sum / &, whi%h is 10 ". 2ote that " / (!11!# and

& / (1!!1#* the are %omplements of ea%h other. $he sender

sends the five data numbers and the %he%sum (7, 11, 1, !,", . If there is no %orruption in transmission, the re%eiver

re%eives (7, 11, 1, !, ", and adds them in one)s

%omplement to get 10 (See Figure below#.

Example 3


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Figure : Example 3


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Procedure to calculate the traditional checksum

error detection and correction.ppt

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