DATA COMMUNICATION Lecture-34.

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Presentation transcript:

DATA COMMUNICATION Lecture-34

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

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

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

Longitudinal Redundancy Check

Example 9.4 Suppose the following block is sent: 10101001 00111001 11011101 11100111 __________ 10101010 (LRC)

Example 9.4 (Cont’d) It is hit by a burst of length 8 and some bits are corrupted: 10100011 10001001 11011101 11100111 __________ 10101010 (LRC)

Example 9.4 (Cont’d) Receiver checks LRC, some of bits do not follow even parity rule and whole block is discarded 10100011 10001001 11011101 11100111 __________ 10101010 (LRC)

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

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

Performance of LRC For Example: Original data units 11110000 11000011 Changed data units 01110001 01000010

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

Cyclic Redundancy Check

Modulo-2 Division in a CRC Generator

Modulo-2 Division in a CRC Checker

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)

Polynomials

Standard Polynomials

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

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

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

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

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