3.6k views

Data transmitted on a link uses the following $2D$ parity scheme for error detection:
Each sequence of $28$ bits is arranged in a $4\times 7$ matrix (rows $r_0$ through $r_3$, and columns $d_7$  through $d_1$) and is padded with a column $d_0$ and row $r_4$ of parity bits computed using the Even parity scheme. Each bit of column $d_0$ (respectively, row $r_4$) gives the parity of the corresponding row (respectively, column). These $40$ bits are transmitted over the data link.

$$\small \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline &\bf{d_7}&\bf{d_6}&\bf{d_5}&\bf{d_4}&\bf{d_3}&\bf{d_2}&\bf{d_1}&\bf{d_0}\\ \hline \bf{r_0}&0&1&0&1&0&0&1&\bf{1}\\\hline \bf{r_1}&1&1&0&0&1&1&1&\bf{0}\\\hline \bf{r_2}&0&0&0&1&0&1&0&\bf{0}\\\hline \bf{r_3}&0&1&1&0&1&0&1&\bf{0}\\\hline \bf{r_4}&\bf{1}&\bf{1}&\bf{0}&\bf{0}&\bf{0}&\bf{1}&\bf{1}&\bf{0}\\ \hline\end{array}$$

The table shows data received by a receiver and has $n$ corrupted bits. What is the mini­mum possible value of $n$?

1. $1$
2. $2$
3. $3$
4. $4$
edited | 3.6k views
+2
is this the  approach to solve this?

i got too many combinations and choose minimum among them

or alternate way ?

$$\small \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline &\bf{d_7}&\bf{d_6}&\bf{d_5}&\bf{d_4}&\bf{d_3}&\bf{d_2}&\bf{d_1}&\bf{d_0}\\ \hline \bf{r_0}&0&1&0&1&0&0&1&\bf{1}\\\hline \bf{r_1}&1&1&\boxed0&0&1&1&1&\bf{0}\\\hline \bf{r_2}&0&0&0&1&0&1&0&\bf{0}\\\hline \bf{r_3}&0&1&1&0&1&0&1&\bf{0}\\\hline \bf{r_4}&\bf{1}&\bf{1}&\bf{0}&\bf{0}&\bf{0}&\boxed{\bf{0}}&\bf{1}&\boxed{\bf{1}}\\ \hline\end{array}$$

Here, we need to change minimum $3$ bits, and by doing it we get correct parity column wise and row wise (Correction marked by boxed number)

edited by
+2

@Prashant but it will be (r1,d0),(r4,d2),(r4,d5)

0
R1d5 R1d1 R1do will also do the work.

Three corrupted columns and one corrupted row will be handled by this
0
0
0
What if we just correct r1d5 I think everthever will fall in to place. All rows and columns will give correct parity won't they??
0

@vupadhayayx86 ....bro you have to again check table after r1d5 correcting . and you will get again corrupted bit.

1. First find all corrupted bit column wise, row wise and

2. check first Row wise and column wise from corrupted bit entry then correct it. (bcz of this condition you can correct 2 bit using 1 bit(entry only )

3. at last check again is there any corrupted bit.

(r1, d5) should be 1.

(r4, d2) should be 0.

(r4, d0) should be 1.
+4
it will be (r1,d0),(r4,d2),,(r4,d5) right?
0
(r4,d5) should be 1. Isn`t the answer should be option d?

OTHER WAY

Here we have odd parity at row r1 and columns d5,d2 and d0.

Now since only 1 row shows error it can be (r1,d0) or (r1,d2) or (r1,d5)-----> any one of the three possible choices.

suppose it is (r1,d2).

Now still we are left with two errors at d0 and d5 but there is no error in any other row. It means error is at same row but two columns d0 and d5 and hence row parity could not detect it.

example- it could be r2,d0 and r2,d5 or r3,d0 and r3,d5 or any such choice.

so we can have minimum three bit error here.

edited by
It is 2D parity scheme and generally we check for 1D parity scheme, i.e., either row and column, so in 2D parity scheme we need to check both row as well as column.

And it is given this is even parity so, whichever column and row is not even parity there is corruption happend

So if you look carefully column d5 it is odd parity so there is one corruption similarly at d2 and in last d0.

So make it even 2D parity we need to change atleast 3 bits

So option C is correct.
–1 vote
3 option c
here the parity bits can also be corrupted, so they asked minimun so when we correct (r0,d0) to 0 and (r0,d5) to 1 then the minimun errors i found are 2, so the answer will be B, correct me if i am wrong
0
Refer :

1
2
3
4
5
6