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 110000100 11001111
00011010 11110110
10000001 01111111
10101101 11100001
11111111 01101101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00011010 11001001 111101000 11110010 1
00010001 01011101 1
10010110 10011010 1
11100111 10001000 0
10010010 00110100 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00101101 11000101 000010011 10001001 0
01011010 11110111 1
00001100 10001000 1
11000100 10101100 1
10101100 00011111 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:
10000100 11001111 0
00011010 11110110 1
10000001 01111111 1
10101101 11100001 1
11111111 01101101 1
01001101 11001010 0
1. The parity bits for the 16 columns is: 01001101 11001010
2. The parity bits for the 5 rows is: 01111
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (9,3):
00011010 11001001 1
11101000 11110010 1
00010001 01011101 1
10010110 10011010 1
11100111 10001000 0
10010010 00110100 0
For figure 3, the bits that were flipped are (8,5) and (16,3):
00101101 11000101 0
00010011 10001001 0
01011010 11110111 1
00001100 10001000 1
11000100 10101100 1
10101100 00011111 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: 0100110111001010
The answer was: 01111
The answer was: 0
The answer was: 9,3
The answer was: No