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 110110111 11111000
01100110 10000101
10101111 00000101
00001010 11001110
00001001 01110001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01101001 11101000 100101111 10111000 1
11100100 11001110 1
01110110 01100010 0
10100010 00011010 0
01111110 11100110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01100000 11011101 001110101 10111110 1
10111110 10111100 1
10111100 01110110 1
01001101 00010000 1
01001010 10111001 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:
10110111 11111000 1
01100110 10000101 1
10101111 00000101 0
00001010 11001110 1
00001001 01110001 0
01111101 11000111 1
1. The parity bits for the 16 columns is: 01111101 11000111
2. The parity bits for the 5 rows is: 11010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (4,0):
01101001 11101000 1
00101111 10111000 1
11100100 11001110 1
01110110 01100010 0
10100010 00011010 0
01111110 11100110 1
For figure 3, the bit that was flipped is (3,3):
01100000 11011101 0
01110101 10111110 1
10111110 10111100 1
10111100 01110110 1
01001101 00010000 1
01001010 10111001 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: 0111110111000111
The answer was: 11010
The answer was: 1
The answer was: 4,0
The answer was: Yes