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 110011111 11100011
00100000 00101101
01110001 01101110
11101101 01000110
01110110 11001001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10010000 01110000 111101011 11100000 0
00011111 11000010 0
10101000 11110011 1
00111111 11000100 1
11110011 01101101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11110011 10111111 111101000 11101110 0
11100011 01100111 1
01100111 11010100 0
00100110 11000111 0
10110001 10100101 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:
10011111 11100011 1
00100000 00101101 1
01110001 01101110 1
11101101 01000110 1
01110110 11001001 1
01010101 00101111 1
1. The parity bits for the 16 columns is: 01010101 00101111
2. The parity bits for the 5 rows is: 11111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (12,1):
10010000 01110000 1
11101011 11100000 0
00011111 11000010 0
10101000 11110011 1
00111111 11000100 1
11110011 01101101 1
For figure 3, the bits that were flipped are (4,3) and (8,2):
11110011 10111111 1
11101000 11101110 0
11100011 01100111 1
01100111 11010100 0
00100110 11000111 0
10110001 10100101 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: 0101010100101111
The answer was: 11111
The answer was: 1
The answer was: 12,1
The answer was: No