Question

explain what is Two-diminution parity check

and give an example

Answer 1

Two Dimensional Parity can detect as well as correct one or more bit errors. If a one or more bit error takes place then the receiver will receive the message with the changed parity bit. It indicates that some error has taken place which means the error is detected.

TWO DIMENSIONAL PARITY: WORKING
We will make a Two Dimensional array from the message bit. After that, according to the even or odd parity, We will fill make the last column and last row of the matrix.

Two Dimensional Parity
Total Parity Bits – i + j + 1 (Row+Column+1)

Here Parity Bit = 3 + 5 +1 = 9

One point is to be Remember that the Value of (i, j ) should be of message array i.e. inspite of having the value of i = 4, j = 6 (which is of array with parity bits). we will take value of message array i.e i=3, j=5.

Row and column parity bits are known as Redundant Bits i.e i+j+1.


 
The code that is to be transmitted will be the whole message included Redundant Bits.
For ex : 

Two Dimensional Parity
Now, this code is transmitted and reaches the receiver side, where the receiver will again form a similar Two Dimensional array.

CASES OCCURS IN TWO DIMENSIONAL PARITY
CASE 1 :
Suppose a bit is in error. Then it can be easily detected and the code is corrected. As shown in fig.

Error Detected
CASE 2 :
When two erroneous bits are detected and corrected. The undesired part is that two other bits also detected as an incorrect bit.

Two Dimensional Parity
CASE 3 :
When odd no. of error takes place in a particular row or particular column.

Two Dimensional Parity
CASE 4 :
When even no. of error takes place in a particular row.

Two Dimensional Parity
CASE 5 :
Where the error is not detected so not corrected.

not detected so corrected
DRAWBACKS
In some cases, an only odd number of bit errors can be detected and corrected but even number of errors can only be detected but not corrected.
In some cases, this method is not able to detect even no bit error.