Question

Consider the data below and implement error detection using VRC and LRC with odd parity. (10 points)

10111100

10001101

01100011

10110111

Answer 1

Using VRC with Odd Parity:

Meaning of ODD Parity is that in a block, total number of 1s will be an odd number.

If in the data, total 1s are odd, 0 is appended as parity bit.
If total 1s are even, 1 is appended as parity bit.

So, for error detection, we just simply count the number of 1s in each block and the result must be an odd number. Then there is no error.

Given data is:

10111100 10001101 01100011 10110111

For block 1: 1011100
Number of 1s = 5 = odd => no error

For block 2: 10001101
Number of 1s = 4 = even => error

For block 3: 01100011
Number of 1s = 4 = even => error

For block 4: 10110111
Number of 1s = 6 = even => error

So, as per the VRC, there is an error in 2^nd, 3^rd and 4^thblock of data. So, the data is invalid here.

Using LRC with Odd Parity:

In LRC, data is organized in a tabular form and then the parity is calculated for each of the column. Here, we are supposed to use odd parity.

As there are 4 blocks received by the receiver, we will arrange first 3 data blocks and count odd parity. After that, we will match it to the last data block which was appended by the sender. using LRC technique.

Or in the simpler way, receiver will arrange the data in the tabular way and calculate number of 1s column wise. For each column, it must be odd number then we can say that there is no error in the data.

Data blocks are: 10111100 10001101 01100011 10110111

Arranging them in table form means:

10111100
10001101
01100011
10110111
-------------
No.of 1s:   31322321

It shows that from the 8 columns, 3 columns are there which are having the total number of 1s as even. So, they are having error i.e. they were modified during transmission so the data is not valid and you should discard this piece of data and ask for retransmission of it.