1. DATA COMMUNICATION
Lecture-34

2. Recap of Lecture 33 Types of Errors Error Detection Techniques
Redundancy
Types of Redundancy Checks
Vertical Redundancy Check (VRC)

3. Overview of Lecture 34 Types of Redundancy Checks
Longitudinal Redundancy Check (LRC)
Cyclic Redundancy Check (CRC)

4. Longitudinal Redundancy Check
A block of bits is divided into rows and a redundant row of bits is added to the whole block

5. Longitudinal Redundancy Check

6. Example 9.4 Suppose the following block is sent: 10101001 00111001
__________
(LRC)

7. Example 9.4 (Cont’d)
It is hit by a burst of length 8 and some bits are corrupted:
__________
(LRC)

8. Example 9.4 (Cont’d)
Receiver checks LRC, some of bits do not follow even parity rule and whole block is discarded
__________
(LRC)

9. Performance of LRC
LRC increases the likelihood of detecting burst errors
An LRC of n bits can
Easily detect a burst error of n bits
Detect more than n bits with a very high probability

10. Performance of LRC One pattern of errors that remains elusive
Two bits in one data unit are damaged
And two bits in exactly the same positions in another data unit are also damaged

11. Performance of LRC For Example: Original data units 11110000 11000011
Changed data units

12. Cyclic Redundancy Check
Uses binary division, not addition
Both sender and receiver use a predetermined divisor (binary number)

13. Cyclic Redundancy Check

14. Modulo-2 Division in a CRC Generator

15. Modulo-2 Division in a CRC Checker

16. Polynomials CRC generator is represented as an polynomial
A polynomial should be selected such that
It should not be divisible by x
It should be divisible by (x+1)

17. Polynomials

18. Standard Polynomials

19. Performance of CRC
CRC can detect all burst errors that affect an odd number of bits
CRC can detect all burst errors of length less than or equal to the degree of the polynomial

20. Performance of CRC
CRC can detect with a very high probability burst errors of length greater than the degree of the polynomial

21. Example 9.6 The CRC-12 ( ) has a degree of 12 It will detect
All burst errors affecting odd no. of bits
All burst errors with a length equal to or less than 12
99.97 % of the time burst errors with a length of 12 or more

22. Summary Types of Redundancy Checks Longitudinal Redundancy Check (LRC)
Cyclic Redundancy Check (CRC)

23. Suggested Reading Section 9.4, 9.5
“Data Communications and Networking” 2nd Edition by Behrouz A. Forouzan