Mumbai University > Information Technology > Sem4 > Computer Networks

Marks: 10M

Year: May 18

Hamming codes are basically linear block codes. It is an error correcting code. The parity bits are inserted in between the data bits as shown below.

Where D-data bits and P- parity bits. The hamming coded data is then transmitter. At the receiver it is coded to get the data back.

The bits $(1,3,5,7),(2,3,6,7)$ and $(4,5,6,7)$ are checked for even parity or odd parity, if all the 4 -bit groups mentioned above possess the even parity (or odd parity) then the received code word is correct but if the parityis not matching then exist. Such error can be located by forming a three bit number out of three parity checks. This process can be well explained by following example,

For example: Suppose a 7 -bit hamming code is received as 1110101 (for transmitter data 1111$)$ and parity used is assumed to be even hence can detect and correct the code as Step1: Received 7 bit hamming code is applied to hamming code format as ![enter image description here][2] Step 2: Check bits for $\mathrm{P} 4$ bit ![enter image description here][3] So $\mathrm{P} 4 = 1$ Step 3: Check bits for $\mathrm{P} 2$bit ![enter image description here][4] So $\mathrm{P} 2= 1$ Step 4: Check bits for $\mathrm{P} 1$ bit ![enter image description here][5] So $\mathrm{P} 1= 0$ Hence the error word is $\mathrm{E}=1 \quad 1 \quad 0$ Step 5: Decimal equivalent of 110 is 6 hence $6^{\text { th }}$ bit is incorrect so invert it and the correct code word will be,

Hence by using this method we can detect as well as correct the error in the transmitted code word. But it can locate a single bit error and fails in detecting the burst error.