Design and Application of Cyclic Redundancy Check Code——Theory, Simulation Analysis and Implementation
A cyclic redundancy check code (Cyclic Redundancy Check, CRC) is a check method widely used in data communication. It detects errors during data transmission by dividing the polynomial generated by the data and appending the remainder to the end of the data. It has important applications in various fields such as computer networks and storage systems.
- theoretical basis
The principle of the CRC code is to process the data bits through an XOR operation to generate a check bit, thereby realizing the integrity verification of the data. Specifically, assuming that the data to be transmitted is D(x), and the CRC generator polynomial is G(x), the calculation process of the CRC check code R(x) is as follows:
First, shift D(x) to the left G(x) times to obtain new data P(x); then, perform modulo 2 division on P(x) and G(x) to obtain the remainder, namely:
P(x) mod G(x) = R(x)
Finally, R(x) is appended to the end of D(x) to form a transmit data frame.
At the receiving end, similarly, shift the received data frame to the left by G(x) bits, and then perform modulo 2 division. If the remainder is 0, there is no error in the data transmission; otherwise, an error occurred.
- Matlab simulation analysis
In Matlab, the CRC check code generator can be generated through the crc.generator function. The specific code is as follows:
poly = [1 0 0 1 1]; %G(x)=x^4+x+1
gen_crc = crc.generator(poly);
data = randi([0,1],1,10);% randomly generated 10-bit data
crcCode = gen_crc(data');% generate CRC check code
tx_signal =