Error Detection and Correction

Now imagine the received data has 7th bit changed from 1 to 0.

Single-bit error

The receiver takes the transmission and recalculates four new data using the same set of bits used by the sender plus the relevant parity (r) bit for each set.

Error detection

Ø  Then it assembles the new parity values into a binary number in order of r position (r8,r4,r2,r1).

Ø  This step gives us the binary number 0111(7 in decimal) which is the precise location of the bit in error.

Ø  Once the bit is identified, the receiver can reverse its value and correct the error.

Hamming Distance

     One of the central concepts in coding for error control is the idea of the Hamming distance.

Ø  The Hamming distance between two words (of the same size) is the number of differences between the corresponding bits. The Hamming distance between two words x and y is d(x, y).

Ø  The Hamming distance can be found by applying the XOR operation on the two words and count the number of 1’s in the result.

Ø  In a set of words, the minimum Hamming distance is the smallest Hamming distance between all possible pairs. We use dmin to define the minimum Hamming distance in a coding scheme.