Introduction[ edit ] CRCs are based on the theory of cyclic error-correcting codes. The use of systematic cyclic codes, which encode messages by adding a fixed-length check value, for the purpose of error detection in communication networks, was first proposed by W. Wesley Peterson in This is important because burst errors are common transmission errors in many communication channels , including magnetic and optical storage devices. Specification of a CRC code requires definition of a so-called generator polynomial. This polynomial becomes the divisor in a polynomial long division , which takes the message as the dividend and in which the quotient is discarded and the remainder becomes the result.
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Why this polynomial? Because there needs to be a standard given polynomial and the standard was set by IEEE Also it is extremely difficult to find a polynomial that detects different bit errors effectively. This is technically called Polynomial Arithmetic. So basically any binary polynomial mod 2 is just addition without carry or XORs.
If you are a hard-core CS-student or engineer I challenge to break this down. Everyone will benefit from this analysis. So to work out a full example: Original message : Polynomial of W idth 4 : Message after appending W zeros : Now we divide the augmented Message by the Poly using CRC arithmetic. The division yields a quotient, which we throw away, and a remainder, which is the calculated checksum. This ends the calculation.
Usually, the checksum is then appended to the message and the result transmitted. In this case the transmission would be: Only use a bit number as your divisor and use your entire stream as your dividend. Throw out the quotient and keep the remainder. Tack the remainder on the end of your message and you have a CRC Average guy review: Take the first 32 bits. Go to step 2. Note that the stream has to be dividable by 32 bits or it should be padded.
For example, an 8-bit ANSI stream would have to be padded. Also at the end of the stream, the division is halted.
Cyclic redundancy check