CONCROL CYNOMIAL CODE, also known as CYCLIC Redundancy Check.

CRC Working method

is generated in the sender A loop redundancy code, which is attached to the receiving end together, and the information received by the receiving end is verified by the same algorithm in the transmitting end to form a cyclic redundancy code.

If it is wrong, Resend.

2. Generation of cyclic redundancy code and code word correctness test example.

CRC check code Algorithm Analysis

CRC check code The encoding method is to be transmitted by binary data T (X) divided by generating polynomial G (X), will last The remainder as a CRC check code.

It acts as follows:

(1) The data block that is sent is the b binary polynomial T (X), (2) generates a polynomial to the R-order G ( x). The end of the data block is added at the end of the data block, and the length of the data block is increased to the M + R bit, and (4) The corresponding binary polynomial is.

(5) is removed by the generation of polynomial G (X), (6), the remainder is the binary polynomial y (x) of the order of R-1. This binary polynomial y (x) is T (X) to generate a CRC check code encoded by polynomial G (X).

(7) subtract Y (x), (8) to obtain a binary polynomial. It is a string to be sent to the CRC check code.

From the CRC encoding rule, the CRC encoding is actually converted to the M-bit binary polynomial T (X) transmitted into a M + R bit binary that can be removed by G (X). The polynomial, so it can be used to remove G (x) when decoding, if the remainder number is zero, then the transmission process is not error; if the remainder is not zero, there is certain an error during the transmission process. Many CRC hardware decoding circuits are detected in this way. It can also be seen as a combination of T (X) and CRC check code, so decoding the received binary data removes the R bit data of the tail, which is the original data.

For a more clear understanding of the encoding process of the CRC check code, the encoding process of the CRC check code is described below with a simple example. Due to the basis of CRC-32, CRC-16, CCITT and CRC-4, only bit numbers and generated polynomial are different.

3. Working principle of cyclic redundancy code

Cycle redundancy CRC When the transmitting end coding and receiving end check, it can utilize the pre-conventional generated polynomial G (X ), The information bits to be transmitted by the K bit may correspond to one (k-1)

secondary polynomial k (x), and the R bit redundancy is corresponding to one (R-1) multiplicity. R (x), the n = k + R bit code characterized by the R bit reduction bit corresponds to one

(N-1) times a multiplicity T (X) = XR * K (X ) + R (x).

4. Features of cyclic redundant check code

1) You can detect all odd bitmads;

2) You can detect all double bits Wrong;

3) You can detect errors that are less than, equal to the length of the check bit.