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 111111110 11100000
11001100 01111001
01111000 01001010
00010110 01111110
01011100 01110111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10011111 11010001 011011101 01000010 0
10110010 00011000 0
11011010 10100001 1
11110011 11000001 1
11011001 11101010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00101110 00001000 100010101 00111111 1
00000011 01110011 0
11000101 00100010 0
11001111 00010110 1
00111010 01110001 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:
11111110 11100000 0
11001100 01111001 1
01111000 01001010 1
00010110 01111110 1
01011100 01110111 0
00000000 11011010 1
1. The parity bits for the 16 columns is: 00000000 11011010
2. The parity bits for the 5 rows is: 01110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (15,3):
10011111 11010001 0
11011101 01000010 0
10110010 00011000 0
11011010 10100001 1
11110011 11000001 1
11011001 11101010 0
For figure 3, the bits that were flipped are (4,5) and (15,2):
00101110 00001000 1
00010101 00111111 1
00000011 01110011 0
11000101 00100010 0
11001111 00010110 1
00111010 01110001 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: 0000000011011010
The answer was: 01110
The answer was: 1
The answer was: 15,3
The answer was: No