E RROR D ETECTION A ND C ORRECTION C ODES Error Detection Code (Parity bit) Error Correction Code ( Hamming Code)

E RRORS While transferring information from one storage media to another, error may occur due to uneven magnetic surface or due to noise or failure. For Example: if transmitter sends 8-bit data But receiver receives 8-bit as due to some noise or some other failure Transmitter Receiver Error

H OW TO DETECT THIS TYPES OF ERRORS ? For detecting such type of errors, we use the method of Parity in which an extra bit known as parity bit or parity check bit is added with the information/word. Now, we can send information or word either using ODD parity or EVEN parity. For ODD parity, the parity bit is so choosen that the total number of 1’s in each information or word is always odd, including the parity bit. And for EVEN parity, the parity bit is so choosen that the total number of 1’s in each information or word is always even, including the parity bit.

O DD /E VEN P ARITY BITS Information/WordOdd Parity (O P )Even Parity (E P )

U SE OF P ARITY B IT In previous example receiver do not know about the error. Because there is no mechanism by which the receiver detect the error. So what is the solution? By using parity bit receiver can easily detect the error (one bit error).

P REVIOUS E XAMPLE WITH P ARITY B IT Suppose we are using ODD Parity System. In order to generate parity bit we have to count the number of 1’s present in the information at transmitting end Transmitter Receiver Error We have 5 Ones (1’s) No of 1’s

P REVIOUS E XAMPLE WITH P ARITY B IT As we are using ODD Parity Bit System, and we have 5 ones (1’s) in the information so the Parity bit is? Answer: 0 The information word with Parity Bit Information/word Parity Bit Information/Word with Parity Bit

S END THIS WORD TO THE RECEIVER Suppose at receiving end the word is received as Now the complete situation is like Transmitter Receiver Error

I NFORMATION AT RECEIVING END How to detect the error at Receiving End? Again count the number of ones (1’s) at Receiving End. As we are using ODD Parity Bit system so according to that we have odd number of 1’s. That means the data at receiving end is not correct Information at Receiving End We Have 4 Ones (1’s) Information at Receiving End No of 1’s

E RROR D ETECTION Now we know that there is some error in the information/word at receiving end. But what is the error and on which bit? How we can detect? By using Hamming codes.

E RROR C ORRECTION C ODE By the use of Parity Bit we can just detect that, the information/word at receiving end is not correct. Because it is Error Detection Code. So the error detection code simple detect either the information/word at receiving end is correct or not. But it can’t correct the information/word. For this we need Error Correction Code. Hamming Code is one of the wall-known error correction Code.

H AMMING C ODE Three Steps Before Transmission. 1. Determine the number of Parity Bits to be added to the given message bits. 2. Determine the position of parity bits. 3. Determine the position checked by the Parity bits.