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 100110000 11100010
10100001 00011011
10111101 10101000
10011000 01001110
00000011 01101000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11010110 11010001 110111001 10101000 0
10110011 11111100 0
10100010 01001010 0
10111000 01101110 1
11000110 10100101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01100100 01001111 000100101 01010110 0
10111101 11010101 1
00111111 10011000 1
00011011 00111101 1
11011100 01101001 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:
00110000 11100010 0
10100001 00011011 1
10111101 10101000 1
10011000 01001110 1
00000011 01101000 1
10110111 01110111 0
1. The parity bits for the 16 columns is: 10110111 01110111
2. The parity bits for the 5 rows is: 01111
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (13,2):
11010110 11010001 1
10111001 10101000 0
10110011 11111100 0
10100010 01001010 0
10111000 01101110 1
11000110 10100101 0
For figure 3, the bits that were flipped are (5,1) and (16,5):
01100100 01001111 0
00100101 01010110 0
10111101 11010101 1
00111111 10011000 1
00011011 00111101 1
11011100 01101001 0
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: 1011011101110111
The answer was: 01111
The answer was: 0
The answer was: 13,2
The answer was: No