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 100001110 01101111
01111010 01111010
11100101 00000110
01111010 01001001
01100110 10001000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00011001 00001111 110110111 11110001 1
11101000 00001001 0
00110010 10110111 1
10101001 10111000 1
11011101 11101000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11011000 11110010 110000110 11100010 1
00010100 01100110 1
10010100 01111000 1
01010110 00010011 1
10001000 00111101 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:
00001110 01101111 1
01111010 01111010 0
11100101 00000110 1
01111010 01001001 0
01100110 10001000 0
10001101 11010010 0
1. The parity bits for the 16 columns is: 10001101 11010010
2. The parity bits for the 5 rows is: 10100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (11,4):
00011001 00001111 1
10110111 11110001 1
11101000 00001001 0
00110010 10110111 1
10101001 10111000 1
11011101 11101000 0
For figure 3, the bit that was flipped is (10,2):
11011000 11110010 1
10000110 11100010 1
00010100 01100110 1
10010100 01111000 1
01010110 00010011 1
10001000 00111101 1
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 1000110111010010
The answer was: 10100
The answer was: 0
The answer was: 11,4
The answer was: Yes