Explain CRC code generation with example.

Decoding the Mystery of CRC Code Generation in Computer Networks

Understanding Cyclic Redundancy Check (CRC)

• CRC is an error-detecting code used in data transmission and storage.
• It ensures data integrity by adding a checksum to the data.
• The checksum is generated using polynomial division.
• Detects burst errors effectively.

The CRC Generation Process

• Choose a generator polynomial (e.g., x⁴ + x + 1). This polynomial is predetermined and agreed upon by sender and receiver.
• Represent the data as a polynomial. For example, the binary data 101100 becomes x⁵ + x³ + x².
• Append zeros to the data polynomial equal to the degree of the generator polynomial (in this case, 4 zeros: 1011000000).
• Perform polynomial long division of the augmented data polynomial by the generator polynomial.
• The remainder from the division is the CRC checksum.
• Append this remainder to the original data to create the transmitted data.

Example: CRC Calculation

• Data: 101100
• Generator Polynomial: x⁴ + x + 1 (10011 in binary)
• Augmented Data: 1011000000
• Polynomial Division: (using modulo-2 arithmetic, where addition and subtraction are equivalent to XOR) will result in a remainder. The steps will involve XORing according to the polynomial division rules.
• Remainder (CRC Checksum): The remainder obtained from the division (e.g. 100). This depends on the chosen polynomial and the data.
• Transmitted Data: Original data + CRC (e.g., 101100100).

CRC Verification at the Receiver

• The receiver performs the same polynomial division on the received data (including the CRC) using the same generator polynomial.
• If the remainder is zero, the data is considered error-free.
• If the remainder is non-zero, an error occurred during transmission.