check code
Check code basics
Code distance: any kind of code consists of many code words, and the binary digits with the least change between any two code words are called the code distance of the data check code
For example: use 4-bit binary to represent 16 states, then there are 16 different code words, at this time the code distance is 1. Such as 0000 and 0001
Parity
Odd parity: the number of "1" in the entire check code (valid information and parity bit) is odd Even
parity: the number of "1" in the entire check code (effective information and parity bit) is an even number
Parity check, can check 1 bit (odd number) error, not error correctable
CRC Cyclic Redundancy Check Code
CRC check, error detectable, not error correctable
Coding method: splicing r-bit check codes after k-bit information codes.
Divide the received CRC code with the agreed generator polynomial G(X) (modulo two division, if correct, the remainder is 0; if a certain bit is wrong, the remainder is not 0
Hamming check code
Add several parity bits to effective information bits to form a Hamming code, so that the code distance is more evenly enlarged, and each binary bit of the Hamming code is assigned to several parity groups. When a certain bit is wrong, it will cause the value of several related parity bits to change, which can not only find the error, but also point out the location of the error, providing a basis for automatic error correction
2^r >= m+r +1
