Error Detection and Correction: Two Dimensional Parity
Suppose that a packet’s payload consists of 10 eight-bit values (e.g., representing ten ASCII-encoded characters) shown below. (Here, we have arranged the ten eight-bit values as five sixteen-bit values):
Figure 111101101 11011001
01100101 01011010
00010010 11000100
10101101 10000110
01101010 10011011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11011100 01101110 101110010 11001101 1
00011111 00000111 0
01010001 01110001 1
01110100 11010101 1
10110100 00000000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00000000 10001100 111000010 10100101 1
10111011 00001001 1
10101001 01111001 1
01001110 00000100 1
10111010 01011101 1
Question List
1. For figure 1, compute the two-dimensional parity bits for the 16 columns. Combine the bits into one string
2. For figure 1, compute the two-dimensional parity bits for the 5 rows (starting from the top). Combine the bits into one string
3. For figure 1, compute the parity bit for the parity bit row from question 1. Assume that the result should be even.
4. For figure 2, indicate the row and column with the flipped bit (format as: x,y), assuming the top-left bit is 0,0
5. For figure 3, is it possible to detect and correct the bit flips? Yes or No
Solution
The full solution for figure 1 is shown below:
11101101 11011001 1
01100101 01011010 0
00010010 11000100 1
10101101 10000110 0
01101010 10011011 1
01011101 01011010 1
1. The parity bits for the 16 columns is: 01011101 01011010
2. The parity bits for the 5 rows is: 10101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (2,0):
11011100 01101110 1
01110010 11001101 1
00011111 00000111 0
01010001 01110001 1
01110100 11010101 1
10110100 00000000 0
For figure 3, the bits that were flipped are (2,5) and (5,2):
00000000 10001100 1
11000010 10100101 1
10111011 00001001 1
10101001 01111001 1
01001110 00000100 1
10111010 01011101 1
5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.
That's incorrect
That's correct
The answer was: 0101110101011010
The answer was: 10101
The answer was: 1
The answer was: 2,0
The answer was: No