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 110110010 10111101
11011100 11011101
10010110 00101110
11011001 10111001
11010010 11000111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101000 00000111 101111001 01000100 0
10000100 11101101 0
01011110 01111000 1
10111000 10001111 1
10110011 01011001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01011010 11000001 101010011 11011110 1
00110010 10000000 0
11011011 00100101 1
11110101 01110001 1
00010101 11011011 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:
10110010 10111101 0
11011100 11011101 1
10010110 00101110 0
11011001 10111001 0
11010010 11000111 1
11110011 00110000 0
1. The parity bits for the 16 columns is: 11110011 00110000
2. The parity bits for the 5 rows is: 01001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (0,1):
00101000 00000111 1
01111001 01000100 0
10000100 11101101 0
01011110 01111000 1
10111000 10001111 1
10110011 01011001 1
For figure 3, the bits that were flipped are (11,1) and (16,4):
01011010 11000001 1
01010011 11011110 1
00110010 10000000 0
11011011 00100101 1
11110101 01110001 1
00010101 11011011 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: 1111001100110000
The answer was: 01001
The answer was: 0
The answer was: 0,1
The answer was: No