GATE | Gate IT 2008 | Question 64

Data transmitted on a link uses the following 2D parity scheme for error detection:
Each sequence of 28 bits is arranged in a 4×7 matrix (rows r0 through r3, and columns d7 through d1) and is padded with a column d0 and row r4 of parity bits computed using the Even parity scheme. Each bit of column d0 (respectively, row r4) gives the parity of the corresponding row (respectively, column). These 40 bits are transmitted over the data link.

The table shows data received by a receiver and has n corrupted bits. What is the mini­mum possible value of n?
(A) 1
(B) 2
(C) 3
(D) 4

Answer: (C)

Explanation: In the given 2D parity matrix, all rows except r_1 have even parity. Therefore there must be atleast 1 bit error in this row.
Also, there are three columns with odd parities (odd parity indicates errors), d_5, d_2 and d_0.
So there must be a minimum of 3 bit errors.
All three errors could have occurred in r_1 or two of these errors could have occurred in any other row. Since r_1 has an odd parity, there is at least one bit-error in this row.
Therefore option (C) is correct.

This explanation is provided by Chirag Manwani.

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