Cyclic Redundancy Check (CRC)

CRC stands for Cyclic Redundancy Check and is a method used for error detection in computer networks. It is widely used in communication protocols, such as Ethernet, to ensure the integrity of transmitted data.

How CRC Works

CRC involves the use of a polynomial division algorithm to generate a checksum for a block of data. This checksum is appended to the data and transmitted along with it. At the receiving end, the same polynomial division algorithm is applied to the received data, including the checksum. If the calculated checksum matches the received checksum, it indicates that the data has been received without errors. However, if the checksums do not match, it suggests that errors have occurred during transmission.

Polynomial Division Algorithm

The polynomial division algorithm used in CRC involves treating the data as a string of bits and dividing it by a predetermined divisor polynomial. The divisor polynomial is typically represented as a binary number and is chosen based on the specific CRC algorithm being used. The division process is performed bit by bit, with each bit being exclusive-ORed (XOR) with the corresponding bit of the divisor. The result of this XOR operation determines whether the next bit of the data should be XORed with the divisor or not. This process continues until all bits of the data have been processed.

Checksum Calculation

The CRC checksum is calculated by performing the polynomial division algorithm on the data, including the appended checksum bits. The remainder obtained from this division is the checksum. The checksum is then appended to the original data and transmitted.

Error Detection

At the receiving end, the same polynomial division algorithm is applied to the received data, including the appended checksum. If the remainder obtained from the division is zero, it indicates that no errors have occurred during transmission. However, if the remainder is non-zero, it suggests that errors have occurred.

Conclusion

CRC is a powerful error detection technique used in computer networks to ensure the integrity of transmitted data. By calculating a checksum using a polynomial division algorithm, CRC can detect errors introduced during transmission. It is a widely used and efficient method for error detection in various communication protocols.