describe the technique of cyclic redundancy checking for error detection in communication system. illustrate your answer by calculating the CRCL Checksum for the data sequence 11110110 using generating polynomial X3+x+1
Answers
Explanation:
Error detection is a technique that is used to check if any error occurred in the data during the transmission.
Some popular error detection methods are-
Single Parity Check
Cyclic Redundancy Check (CRC)
Checksum
In this article, we will discuss about Cyclic Redundancy Check (CRC).
Cyclic Redundancy Check-
Cyclic Redundancy Check (CRC) is an error detection method.
It is based on binary division.
CRC Generator-
CRC generator is an algebraic polynomial represented as a bit pattern.
Bit pattern is obtained from the CRC generator using the following rule-
The power of each term gives the position of the bit and the coefficient gives the value of the bit.
Example-
Consider the CRC generator is x7 + x6 + x4 + x3 + x + 1.
The corresponding binary pattern is obtained as-
Thus, for the given CRC generator, the corresponding binary pattern is 11011011.
Properties Of CRC Generator-
The algebraic polynomial chosen as a CRC generator should have at least the following properties-
Rule-01:
It should not be divisible by x.
This condition guarantees that all the burst errors of length equal to the length of polynomial are detected.
Rule-02:
It should be divisible by x+1.
This condition guarantees that all the burst errors affecting an odd number of bits are detected.
Important Notes-
If the CRC generator is chosen according to the above rules, then-
CRC can detect all single-bit errors
CRC can detect all double-bit errors provided the divisor contains at least three logic 1’s.
CRC can detect any odd number of errors provided the divisor is a factor of x+1.
CRC can detect all burst error of length less than the degree of the polynomial.
CRC can detect most of the larger burst errors with a high probability.
Steps Involved-
Error detection using CRC technique involves the following steps-