This document provides an overview of CRC (Cyclic Redundancy Check) and checksum techniques for error detection in data transmission. It describes how CRC works by appending redundant bits to the data such that the resulting data is divisible by a predetermined binary number. It also explains how checksums are generated by dividing the data into sections, adding the sections using one's complement arithmetic, and sending the complement of the sum along with the data. The document compares the performance of CRC and checksums, noting that CRC can detect all odd-length burst errors while checksums are susceptible to some even-length errors.

1. DATA COMMUNICATIONS &
NETWORKING
LECTURE-
21
Course Instructor : Sehrish Rafiq
Department Of Computer Science
University Of Peshawar

2. LECTURE OVERVIEW
 CRC
 Performance of CRC
 Checksum
 Performance of Checksum

3. ERROR DETECTION METHODS

4. CYCLIC REDUNDANCY CHECK
 The third and the most powerful technique is CRC.
 CRC is based on binary division.
 In CRC a sequence of redundant bits called the CRC
or CRC remainder is appended to the end of a data
unit.
 So that the resulting data unit becomes exactly
divisible by a second, predetermined binary number.
 At the destination, the incoming data unit is divided
by the same number.

5. CYCLIC REDUNDANCY CHECK
 If at this step there is no remainder the data unit
is assumed to be intact and is accepted.
 A remainder indicates that the data unit has
been damaged in transit and therefore must be
rejected.

6. REDUNDANCY BITS
 The redundancy bits used by CRC are derived by
dividing the data unit by a predetermined
divisor,the remainder is the CRC.
 To be valid, a CRC must have two qualities.
 It must have exactly one less bit than the divisor.
 Appending it to the end of the data string must
make the resulting bit sequence exactly divisible
by the divisor.

7. CRC GENERATOR & CHECKER

8. BINARY DIVISION IN A CRC
GENERATOR

9. BINARY DIVISION IN CRC
CHECKER

10. HOW IT WORKS???
 At the Transmitter:
 Step 1: A string of n 0’s is appended to the data
unit.
 The number n is 1 less than the number of bits in the
predetermined divisor which is n+1 bits.
 Step 2: The newly elongated data unit is divided
by the divisor using a process called binary
division.
 The remainder resulting from this division is the CRC.
 Step 3: The CRC derived in step 2 replaces the
appended 0’s at the end of the data unit.

11. HOW IT WORKS???
 At the receiver:
 The data unit arrives at the receiver data first
followed by the CRC.
 Step 1: The receiver treats the whole string as a
unit and divides it by the same divisor that was
used to find the CRC remainder.
 Result:
 If the string arrives without error ,the CRC checker yields
a remainder of 0 and the data unit passes.
 If the string has been changed in transit ,the division
yields a non zero remainder and the string passes.

12. THE CRC DIVISOR
 The divisor in the CRC generator is most often
represented not as a string of 1’s and 0’s but as
an algebraic polynomial.
 A polynomial should be selected to have at least
the following properties:
 It should not be divisible by x.
 It should be divisible by x+1.
 E.g.

13. A POLYNOMIAL
REPRESENTING A DIVISOR

14. STANDARD POLYNOMIALS
Name Polynomial Application
CRC-8CRC-8 x8
+ x2
+ x + 1 ATM header
CRC-10CRC-10 x10
+ x9
+ x5
+ x4
+ x2
+ 1 ATM AAL
ITU-16ITU-16 x16
+ x12
+ x5
+ 1 HDLC
ITU-32ITU-32
x32
+ x26
+ x23
+ x22
+ x16
+ x12
+ x11
+ x10
+ x8
+ x7
+ x5
+ x4
+ x2
+ x + 1
LANs

15. PERFORMANCE OF CRC
 CRC can detect all burst errors that effect an
odd number of bits.
 CRC can detect all burst errors of length less
than or equal to the degree of polynomial.
 CRC can detect with a very high probability
,burst errors of length greater than the degree of
polynomial.

16. CHECKSUM
 The checksum is also based on the concept of
redundancy.

17. CHECKSUM GENERATOR
 The sender follows these steps:
 Step 1: The unit is divided in to k sections, each
of n bits.
 Step 2: All sections are added using one’s
complement to get the sum in such a way that
the total is also n bits long.
 Step 3: The sum is then complemented and
becomes the checksum.
 Step 4: The checksum is sent with the data.

18. CHECKSUM CHECKER
 The sender follows these steps:
 Step 1: The unit is divided in to k sections, each
of n bits.
 Step 2: All sections are added using one’s
complement to get the sum in such a way that
the total is also n bits long.

 Step 3: The sum is then complemented.
 Step 4: If the result is zero, the data are
accepted, otherwise they are rejected.

19. CHECKSUM

20. DATA UNIT AND CHECKSUM

21. Example 1Example 1
Suppose the following block of 16 bits is to be sent using a
checksum of 8 bits.
10101001 00111001
The numbers are added using one’s complement
10101001
00111001
------------
Sum 11100010
Checksum 00011101
The pattern sent is 10101001 00111001 00011101

22. EXAMPLE 1 CONTINUED…
Now suppose the receiver receives the pattern sent 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.

23. EXAMPLE 1 CONTINUED…
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 1 11000101
Carry 1
Sum 11000110
Complement 00111001 the pattern is corrupted.

24. PERFORMANCE OF CHECKSUM
 The checksum detects all errors involving an odd
number of bits as well as most errors involving
an even number of bits.
 However 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 a
problem.
 Checksum retains all carriers, so although two 0s
becoming 1 would not alter the value of their own
column,it would change the value of the next
higher column.

25. THANKS!!!