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 101111000 11001010
10100011 10001000
00101010 10011101
10010001 10111000
11111011 11011011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10110110 01000110 000111010 10101010 0
11000110 10001000 0
01010111 11010110 0
10110010 01101111 0
10100111 11011101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01111110 11110100 111001001 00101101 0
11011101 01001100 0
01010000 10001010 1
11111001 00001111 0
11000011 00011000 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:
01111000 11001010 0
10100011 10001000 0
00101010 10011101 0
10010001 10111000 1
11111011 11011011 1
10011011 10111100 0
1. The parity bits for the 16 columns is: 10011011 10111100
2. The parity bits for the 5 rows is: 00011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (4,5):
10110110 01000110 0
00111010 10101010 0
11000110 10001000 0
01010111 11010110 0
10110010 01101111 0
10100111 11011101 0
For figure 3, the bit that was flipped is (12,2):
01111110 11110100 1
11001001 00101101 0
11011101 01001100 0
01010000 10001010 1
11111001 00001111 0
11000011 00011000 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: 1001101110111100
The answer was: 00011
The answer was: 0
The answer was: 4,5
The answer was: Yes