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 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), , and .
So there must be a minimum of 3 bit errors.
All three errors could have occurred in or two of these errors could have occurred in any other row. Since 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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