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 100001001 10100101
11010001 10100001
10100011 00001110
00101010 01000011
11100111 10001010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110111 10111100 001100110 01110000 1
00111101 11000100 1
10111011 11101101 0
01001100 10111110 1
01111011 01011011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10101101 01010000 110010000 11101111 1
01001111 01010000 1
01100110 00001010 0
01010110 11000010 1
01100010 00100111 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:
00001001 10100101 0
11010001 10100001 1
10100011 00001110 1
00101010 01000011 0
11100111 10001010 1
10110110 11000011 1
1. The parity bits for the 16 columns is: 10110110 11000011
2. The parity bits for the 5 rows is: 01101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (2,2):
11110111 10111100 0
01100110 01110000 1
00111101 11000100 1
10111011 11101101 0
01001100 10111110 1
01111011 01011011 1
For figure 3, the bit that was flipped is (2,5):
10101101 01010000 1
10010000 11101111 1
01001111 01010000 1
01100110 00001010 0
01010110 11000010 1
01100010 00100111 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: 1011011011000011
The answer was: 01101
The answer was: 1
The answer was: 2,2
The answer was: Yes