Error Detection & Error Correction

1. Error Detection & Error Correction
Computer Networks

2. Team Members
Group-I Assignment Topic : Error Detection & Error Correction
Group's representative: TANGUTURU SAI KRISHNA
S.No. BITS ID NAME Official Email ID Personal Email ID
1 2011HW69898
TANGUTURU SAI KRISHNA saikrishna.tanguturu@wipro.com sai.tsk2008@gmail.com
2 2011HW69900
RAYAPU MOSES rayapu.moses@wipro.com stalinkvd001@gmail.com
3 2011HW69932 SHENBAGAMOORTHY A
shenbagamoorthy.a83@wipro.com moorthy2626@gmail.com
4 2011HW69913
ANURUPA K C anurupa.c85@wipro.com anu.rupa30@gmail.com
5 2011HW69909
ARUNJUNAISELVAM P arunjunaiselvam.p95@wipro.com arunjunai.carrer@gmail.com
6 2011HW69569
PRANOB JYOTI KALITA pranob.kalita@wipro.com pranob.kalita90@gmail.com
7 2011HW69893
TINNALURI V N PRASANTH prasanth.tinnaluri@wipro.com naga.prasanth985@gmail.com
8 2011HW69904
KONDALA SUMATHI sumathi.kondala@wipro.com sumathi.kondala@gmail.com
9 2011HW69896
DASIKA KRISHNA dasika.krishna@wipro.com dasikakrishnas@gmail.com
10 2011HW69907
SHEIK SANAVULLA sheik.sanavulla@wipro.com sanavulla.sms@gmail.com
11 2011HW70163
K ASWINI PRIYANKA kamma.priyanka@wipro.com ashupriya.priyanka6@gmail.com
12 2011HW70828
BODDU MADHAVI REDDY boddu.reddy@wipro.com mreddy786@gmail.com

3. 3
Data Link Layer

4. Definition of Error
 Networks must be able to transform data
from once device to another with
complete accuracy. While the
transmission data can be corrupted, for
reliable communication errors must be
detected and corrected.

5. 5
Types of Errors
 Single-bit errors
 Burst errors

6. 6
Redundancy
 To detect or correct errors, redundant bits of data
must be added

7. Detection/Correction Techniques
 Parity Checks
 Checksumming methods
 Cyclic redundancy checks

8. Parity Checks
Parity Bit (PB)
One additional bit per character
Even parity
Odd Parity

9. How many bit errors can PB detect ?
10001110 --- 10101110 => error !
10001110 --- 10100110 => No error detected !!!
Conclusion – 1 PB can only detect an odd number of
errors !

10. Single Bit Error Correction
Parity for each character(byte=line) + parity for each column (set of data
bytes sent)

11. Example - Single Bit Error Correction
Hamming - Correctable single bit error

12. 12
Cyclic Redundancy Checksum (CRC)
•CRC error detection method treats packet of data to
be transmitted as a large polynomial
•Transmitter
•Using polynomial arithmetic, divides polynomial by a
given generating polynomial
•Quotient is discarded
•Remainder is “attached” to the end of message

13. 13
Cyclic Redundancy Checksum
(continued)
•Message (with the remainder) is transmitted to the
receiver
•Receiver divides the message and remainder by
same generating polynomial
•If a remainder not equal to zero results  error
during transmission
•If a remainder of zero results  error during
transmission

14. 14
CRC Encoder/Decoder

15. CRC - Example
Frame – 1101011011
G(x)=x4+x+1
Transmitted frame:
11010110110000 –
00000000001110
----------------------
11010110111110

16. Checksums
 • A checksum “adds” together “chunks” of data
 – The “add” operation may not be normal integer
addition
 – The chunk size is typically 8, 16, or 32 bits
 • We’ll discuss:
 – Integer addition “checksum”
 – One’s complement “checksum”
 – Fletcher Checksum
 – Adler Checksum
 – ATN Checksum (AN/466)

17. 17
Error Correction
 Two methods
 Retransmission after detecting error
 Forward error correction (FEC)

18. 18
Forward Error Correction
 Consider only a single-bit error in k bits of data
 k possibilities for an error
 One possibility for no error
 #possibilities = k + 1
 Add r redundant bits to distinguish these
possibilities; we need
2r  k+1
 But the r bits are also transmitted along with
data; hence
2r  k+r+1

19. 19
Number of Redundant Bits
Number of
data bits
k
Number of
redundancy bits
r
Total
bits
k + r
1 2 3
2 3 5
3 3 6
4 3 7
5 4 9
6 4 10
7 4 11

20. 20
Hamming Code
 Simple, powerful FEC
 Widely used in computer memory
 Known as ECC memory
error-correcting bits

21. 21
Redundant Bit Calculation

22. 22
Example: Hamming Code

23. Thank You
Saikrishna Tanguturu