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 111111110 11111100
01000010 11011011
00000011 01010110
11100011 00101101
11111110 00011001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10110010 01101111 011000010 00101011 1
00000001 11100110 0
10111011 00010000 0
00111100 00101000 0
11110110 00011010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00011111 10011101 001101011 11001011 0
00000111 01010110 1
01110111 00100100 0
10011101 01100110 1
10010001 01000010 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:
11111110 11111100 1
01000010 11011011 0
00000011 01010110 0
11100011 00101101 1
11111110 00011001 0
10100010 01000101 0
1. The parity bits for the 16 columns is: 10100010 01000101
2. The parity bits for the 5 rows is: 10010
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (8,3):
10110010 01101111 0
11000010 00101011 1
00000001 11100110 0
10111011 00010000 0
00111100 00101000 0
11110110 00011010 1
For figure 3, the bit that was flipped is (4,5):
00011111 10011101 0
01101011 11001011 0
00000111 01010110 1
01110111 00100100 0
10011101 01100110 1
10010001 01000010 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: 1010001001000101
The answer was: 10010
The answer was: 0
The answer was: 8,3
The answer was: Yes