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 110110101 10010001
10111101 00010111
10101110 10000010
00011100 00001101
11001101 01101100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01101111 01011000 111101011 10111110 0
01101110 10101010 1
11000010 00011101 0
10001001 11000011 1
10110001 10010010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10110111 01010011 101000110 00111110 0
01111001 11000011 1
01100111 00011010 0
01101011 11010101 0
10000100 01110001 0
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:
10110101 10010001 0
10111101 00010111 0
10101110 10000010 1
00011100 00001101 0
11001101 01101100 1
01110111 01100101 0
1. The parity bits for the 16 columns is: 01110111 01100101
2. The parity bits for the 5 rows is: 00101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (3,3):
01101111 01011000 1
11101011 10111110 0
01101110 10101010 1
11000010 00011101 0
10001001 11000011 1
10110001 10010010 1
For figure 3, the bit that was flipped is (11,0):
10110111 01010011 1
01000110 00111110 0
01111001 11000011 1
01100111 00011010 0
01101011 11010101 0
10000100 01110001 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0111011101100101
The answer was: 00101
The answer was: 0
The answer was: 3,3
The answer was: Yes