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 101000101 10111111
11000010 00101110
10000011 11001011
01010011 10111111
11100011 11101000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10010110 01110111 001011010 11000011 0
01000110 01100110 1
01011101 10000001 1
11100100 00000011 0
10110011 01010000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00000010 01000010 100011110 10010100 1
00001100 10000010 0
01100101 01011000 0
00000001 11001010 0
01110000 11000110 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:
01000101 10111111 0
11000010 00101110 1
10000011 11001011 0
01010011 10111111 1
11100011 11101000 1
10110100 00001101 1
1. The parity bits for the 16 columns is: 10110100 00001101
2. The parity bits for the 5 rows is: 01011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (0,5):
10010110 01110111 0
01011010 11000011 0
01000110 01100110 1
01011101 10000001 1
11100100 00000011 0
10110011 01010000 0
For figure 3, the bits that were flipped are (5,3) and (16,4):
00000010 01000010 1
00011110 10010100 1
00001100 10000010 0
01100101 01011000 0
00000001 11001010 0
01110000 11000110 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: 1011010000001101
The answer was: 01011
The answer was: 1
The answer was: 0,5
The answer was: No