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 101010010 00111101
00100010 10100101
01110001 11100110
10001101 00000000
10001010 11001001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01101011 01100110 100001011 11010101 0
00010100 11011001 1
10000000 11010000 1
00110100 01101110 0
11000000 11010101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01010001 11111111 100001101 00011000 0
10111010 10111101 0
01001001 10110110 0
11110000 01100001 1
11011101 10001101 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:
01010010 00111101 0
00100010 10100101 0
01110001 11100110 1
10001101 00000000 0
10001010 11001001 1
00000110 10110111 0
1. The parity bits for the 16 columns is: 00000110 10110111
2. The parity bits for the 5 rows is: 00101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (15,3):
01101011 01100110 1
00001011 11010101 0
00010100 11011001 1
10000000 11010000 1
00110100 01101110 0
11000000 11010101 1
For figure 3, the bits that were flipped are (0,1) and (6,2):
01010001 11111111 1
00001101 00011000 0
10111010 10111101 0
01001001 10110110 0
11110000 01100001 1
11011101 10001101 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: 0000011010110111
The answer was: 00101
The answer was: 0
The answer was: 15,3
The answer was: No