Dear Mouadh,
welcome!
The number of bits n required to correct a single error in a hamming code for a message having m bits can be determined from the equation:
2^n => m+n+1,
For more information please refer to the book> Advanced communication systems, By G. Tomazi.
Best wishes
For 15 data bits it is not possible to have a perfect Hamming code and this would be a poor choice of block length. However the short answer to your question would be 5, 5 bits allow the code to provide the location of the error out of 20 possibilities (15 message and 5 parity). There is more information on the Wikipedia entry for Hamming codes.
In the Hamming code 4 control bits in 15-bits transmitted are needed for correct the single errors , then 11 bits will be as information bits.
Vasyl has highlighted a problem with the question, when you say "
in 15-bits transmited?" do you mean 15 information bits as I have assumed (m in Abdelhalim Zekry's answer) or a total block length of 15 bits as Vasyl has assumed (n in Abdelhalim Zekry's answer) ? This highlights the need for precise language when dealing with error correcting codes.
I understood from the question that the total block length is equal to15 bits.
as vasyl mentioned ,when we say transmited means we aer talking about the block length of the message because we already transmited it !
thats the main problem with the question , should we assume that 15bits transmited means informations bits or block length ?
thanks
If there are 15 information bits (i.e. useful bit), then it is necessary to have 5 control (check) bits and the total block length is equal to 20 bits. Such a code is called a shortened Hamming code. If there are 25 information bits or more, then it is necessary 6 control (check) bits, etc.
I will clarify my answer. 5 check bits are required if the number of information bits is equal to 12, 13, 14, 15, …, 26.
- Badges
- Science topic
- Similar topics
- Correction