Hamming Code - Error correction

Hamming Code - Error correction

When sender sends data to receiver, but if sender data and receiver data does not match then it is called error. Error can be handled in two ways, first solution is re-transmission of data, and second error is corrected on the receiver side.

A receiver can use error correcting code and this code corrects data automatically.

A single bit error can be correct using parity bit.

Multiple bit error can be correct using hamming code.

HAMMING CODE

Hamming code was invented by Richard Hamming in 1950. Hamming code can detect up to 2-bit error. Hamming code uses a redundancy code, and these redundant bits is used to correct data. If data is of m bit and redundant bit is of r bit, then total data to be sent is m+r.

If the total number of transmittable bit is m+r, then r must be able to represents m+r+1 different state.

2^r >= m+r+1

If value of m is 7 then minimum value of r is 4.

Now the question is the position of redundant bits (r). Each redundant bit is placed on power of 2. For example, redundant bit0 will placed on 2⁰, redundant bit1 will placed on 2¹ and so on.

The values of redundant bits is determined by combinations of data bits
r1 = bits 1,3,5,7,9,11
r2 = bits 2,3,6,7,10,11
r3 = bits 4,5,6,7
r4 = bits 8,9,10,11