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 00011000
11011001 00101010
00011100 01010010
11011011 00011001
01010001 10010110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01110101 11010111 101110111 10110001 0
00000010 01101101 0
10111100 00000010 0
00001000 10110110 0
10111100 10111111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11010100 01101000 000111011 10000110 0
01001110 01100100 1
00101110 01101011 1
01110010 10010111 1
10111101 01010110 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 00011000 0
11011001 00101010 0
00011100 01010010 0
11011011 00011001 1
01010001 10010110 1
10100010 11101111 0
1. The parity bits for the 16 columns is: 10100010 11101111
2. The parity bits for the 5 rows is: 00011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (4,5):
01110101 11010111 1
01110111 10110001 0
00000010 01101101 0
10111100 00000010 0
00001000 10110110 0
10111100 10111111 1
For figure 3, the bits that were flipped are (10,0) and (1,5):
11010100 01101000 0
00111011 10000110 0
01001110 01100100 1
00101110 01101011 1
01110010 10010111 1
10111101 01010110 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: 1010001011101111
The answer was: 00011
The answer was: 0
The answer was: 4,5
The answer was: No