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 110010000 00110010
01101100 10100000
00011010 11001010
01001111 00110110
11101000 01000001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10101101 01100101 100000011 10000011 1
01010010 00100110 0
01010011 01110111 0
11101100 01011101 0
01000001 11101010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00111001 10110011 111110010 00010011 1
11000011 10100110 0
00010000 11100101 0
11100010 01110001 1
01111010 10010000 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:
10010000 00110010 1
01101100 10100000 0
00011010 11001010 1
01001111 00110110 1
11101000 01000001 0
01000001 00101111 1
1. The parity bits for the 16 columns is: 01000001 00101111
2. The parity bits for the 5 rows is: 10110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (6,5):
10101101 01100101 1
00000011 10000011 1
01010010 00100110 0
01010011 01110111 0
11101100 01011101 0
01000001 11101010 0
For figure 3, the bits that were flipped are (0,4) and (14,1):
00111001 10110011 1
11110010 00010011 1
11000011 10100110 0
00010000 11100101 0
11100010 01110001 1
01111010 10010000 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: 0100000100101111
The answer was: 10110
The answer was: 1
The answer was: 6,5
The answer was: No