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（1） For example, the data transmitted is 0 and 1, These are two legal codes , from 1 The switch to 0 You only need to convert one bit code , At this time, it is impossible to detect errors , That is, the code distance is 1 It is impossible to detect errors ;

（2） But if use 00 Express 0,11 Express 1, take 00 Switch to 11 Need to change two , If at this time 00 become 01, The system can check for errors , The existing code distance is 2 Error detection can be carried out ;

Illustrate with examples 2- The code distance is 2：

（1） Blue on the first floor 1 Conference room ; Red on the second floor 2 Conference room ;

（2） if ： Go to the blue 2 Conference room , The system cannot check for errors ; Because blue and 2 Conference room is full of correct information ;

2、 error correction

Find the error , And correct the error ;
Illustrate with examples - The code distance is 2

（1） For example, the data transmitted is 00 and 11（00 Corresponding decimal system 0,11 Corresponding decimal system 1）, If you want to 0 convert to 1, You need to 00 convert to 11;

（2） Then in the process of conversion, if 01, You can check for errors ;

（3） However, it is impossible to judge that this is going to 00 turn 11, Or will it 11 turn 00, So I'm not sure about the modification 01 Medium 0 still 1;

（4） So the code distance is 2 Time cannot be corrected ;

Illustrate with examples - The code distance is 3

（1） For example, the data transmitted is 000 and 111（000 Corresponding decimal system 0,111 Corresponding decimal system 1）, If you want to 0 convert to 1, You need to 000 convert to 111;

（2） Then in the process of conversion, if 011, You can check for errors ;

（3） You can also judge , This is to 000 Convert to 111, So it will 011 Medium 0 Corrected to 1;

（4） So the code distance is greater than or equal to 3 when , You can correct it ;

Illustrate with examples 3- The code distance is 3：

（1） Blue on the first floor 1 Conference room ; Red on the second floor 2 Conference room ;

（2） if ： Go to the blue one on the first floor 2 Conference room , At this point, the system can check the error , The first floor and the blue ones are the correct information , Only the name of the conference room is wrong , It will be automatically corrected to blue on the first floor 1 Conference room ;

3、 Yardage

The distance between two legal codes ;
It will affect error correction and detection ;

Two 、 Parity check

1、 Examination site

Coding mechanism ;

2、 Odd check

Only error detection , Can be detected 1（ Odd number ） Dislocation ;
Illustrate with examples

（1） For example, transmitting data 001, When performing odd check , A check bit will be added before the highest bit , Make the coding system 1 The number of is odd ;

（2）001 in , Yes 1 individual 1, So add 0, Turn into 0001;

（3） If at this time 0001 become 0101, Odd check will find ,1 The number of is not odd , So we can check the error ;

（4） In fact, by adding the check digit , Divide the data into verification part and data part , So when the data changes , Both the verification part and the data part of the data will change ; At this time, the code distance is 2, Therefore, errors can be detected ;

3、 Even check

Only error detection , Can be detected 1（ even numbers ） Dislocation ;
Illustrate with examples

（1） For example, transmitting data 001, When performing parity check , A check bit will be added before the highest bit , Make the coding system 1 The number of is even ;

001 in , Yes 1 individual 1, So add 1, Turn into 1001, bring 1 The number of becomes 2 individual ;

If at this time 1001 become 1101, Even check will find ,1 The number of is not even , So we can check the error ;

3、 ... and 、CRC（ Cyclic redundancy check ）

1、 Examination site

Data structure ;
model 2 except ;
In the soft exam, I think CRC Error correction is not allowed, only error detection , because CRC Not 100% error correction ; Only when the generated polynomial design is perfect , In order to correct the error ;

2、 principle

Use data and generated polynomials as modules 2 In addition to the operation , Check bits are generated , Write the check bit and the data bit together to produce a code （ Data bits in front , The check digit is after ）;