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 110011010 00010100
10110101 11010011
00010011 11011011
01111111 10110111
11111001 01011001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00100001 11100000 100101110 01110001 0
01100001 11011011 0
11011101 10110100 0
00111010 10010100 1
10011001 01101010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10010011 10110101 110100011 01101111 0
10110010 00110101 1
10110000 00100101 1
10000100 10000010 0
11110010 01001000 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:
10011010 00010100 0
10110101 11010011 0
00010011 11011011 1
01111111 10110111 1
11111001 01011001 0
10111010 11110010 0
1. The parity bits for the 16 columns is: 10111010 11110010
2. The parity bits for the 5 rows is: 00110
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (3,2):
00100001 11100000 1
00101110 01110001 0
01100001 11011011 0
11011101 10110100 0
00111010 10010100 1
10011001 01101010 0
For figure 3, the bits that were flipped are (5,2) and (1,3):
10010011 10110101 1
10100011 01101111 0
10110010 00110101 1
10110000 00100101 1
10000100 10000010 0
11110010 01001000 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: 1011101011110010
The answer was: 00110
The answer was: 0
The answer was: 3,2
The answer was: No