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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