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 101000001 11100011
01010101 00000000
10101011 00111100
01001010 11111100
10110010 01100010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110101 01010011 001111100 11111100 1
11111000 11000010 1
01111111 11011011 1
01010110 10100000 0
01011000 10010110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00011111 10000100 100101011 00110001 1
10110101 01100010 0
11110111 10010110 1
10101111 01101001 0
10011001 00101000 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:
01000001 11100011 1
01010101 00000000 0
10101011 00111100 1
01001010 11111100 1
10110010 01100010 1
01000111 01000001 0
1. The parity bits for the 16 columns is: 01000111 01000001
2. The parity bits for the 5 rows is: 10111
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (8,2):
11110101 01010011 0
01111100 11111100 1
11111000 11000010 1
01111111 11011011 1
01010110 10100000 0
01011000 10010110 1
For figure 3, the bit that was flipped is (1,5):
00011111 10000100 1
00101011 00110001 1
10110101 01100010 0
11110111 10010110 1
10101111 01101001 0
10011001 00101000 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: 0100011101000001
The answer was: 10111
The answer was: 0
The answer was: 8,2
The answer was: Yes