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 100101000 01100101
11111000 00001000
01110111 11100110
10110110 00011011
11101111 11111110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10001001 00111111 110110001 00000100 0
10110110 01000001 1
00010101 01110101 0
10001100 10111000 1
01010111 10110111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11101010 00010110 111100000 00100010 1
11000110 00000101 0
01011011 00001110 0
11001101 00001011 0
01010010 00110100 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:
00101000 01100101 0
11111000 00001000 0
01110111 11100110 1
10110110 00011011 1
11101111 11111110 0
11111110 01101110 0
1. The parity bits for the 16 columns is: 11111110 01101110
2. The parity bits for the 5 rows is: 00110
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (1,1):
10001001 00111111 1
10110001 00000100 0
10110110 01000001 1
00010101 01110101 0
10001100 10111000 1
01010111 10110111 1
For figure 3, the bit that was flipped is (4,0):
11101010 00010110 1
11100000 00100010 1
11000110 00000101 0
01011011 00001110 0
11001101 00001011 0
01010010 00110100 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: 1111111001101110
The answer was: 00110
The answer was: 0
The answer was: 1,1
The answer was: Yes