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 100111111 01111100
00001001 00110111
10111000 00010100
00110000 11111000
01000011 11010001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01111101 11100100 000010101 10101110 0
11000010 01111111 0
11001110 11001111 1
11110001 00000011 0
10010101 01111001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01111101 11100000 101101010 11010111 0
10001010 11001111 1
11111100 00111110 1
00011100 10101010 0
01111001 01101110 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:
00111111 01111100 1
00001001 00110111 1
10111000 00010100 0
00110000 11111000 1
01000011 11010001 1
11111101 01110110 0
1. The parity bits for the 16 columns is: 11111101 01110110
2. The parity bits for the 5 rows is: 11011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (8,4):
01111101 11100100 0
00010101 10101110 0
11000010 01111111 0
11001110 11001111 1
11110001 00000011 0
10010101 01111001 1
For figure 3, the bits that were flipped are (14,4) and (5,5):
01111101 11100000 1
01101010 11010111 0
10001010 11001111 1
11111100 00111110 1
00011100 10101010 0
01111001 01101110 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: 1111110101110110
The answer was: 11011
The answer was: 0
The answer was: 8,4
The answer was: No