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Coding of Hamming
Principle of Coding
The coding of Hamming consists in placing bits of coding all the bits 2 ª (1,2,4,8,16, etc.), and in placing the bits of data in the free places.
Example :
Transmission Data
Coded message :
How to determine the value of every bit of control ?
Every bit of control is coded in the following way :
- For the bit C1, we take all the bits 2i +1 of the coded message (1,3,5, etc.). We have a continuation : we take a bit which will serve for determining the value of C1, we jump one, we take the other one, we jump one, etc. This till the end of the message. The sum must be even (thus equal to 0). But in certain cases, she can be odd (and then the sum will have to be equal to 1). Then we are brought to determine the value of C1 so that the sum is even.
- For the bit C2, we take alle the bits 4i +2 of the coded message (2,3,4,5, etc. ). We have a continuation : we take two bits which will serve for determining the value of C2, we jump two, we take it two others, we jump two … This till the end of the message. We are then brought as previously to determine the value of C2 according to the value of the sum and the parity.
- -For the bit Cn, we take all the bits 2ki+k of the message coded with k the number of the bit 2n, and i a variable which increments to obtain the continuation(suite) of the bits used for the coding and those who will not be him.
The coding was made, it does not more remain than to send the message to the canal of transmission.
