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 110010011 11110001
10010111 01100011
11100010 01110010
10100010 00010000
11100101 00010011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11010000 00101011 110111111 00100010 1
00101011 11100100 0
00111000 11010010 1
11000100 11100010 0
10111000 11011001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01000100 10101110 111010101 11110000 1
11000100 00100100 0
10100010 01100011 0
10101000 01011000 0
01001111 01010001 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:
10010011 11110001 1
10010111 01100011 1
11100010 01110010 0
10100010 00010000 0
11100101 00010011 0
10100001 11100011 0
1. The parity bits for the 16 columns is: 10100001 11100011
2. The parity bits for the 5 rows is: 11000
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (13,4):
11010000 00101011 1
10111111 00100010 1
00101011 11100100 0
00111000 11010010 1
11000100 11100010 0
10111000 11011001 1
For figure 3, the bits that were flipped are (3,3) and (11,2):
01000100 10101110 1
11010101 11110000 1
11000100 00100100 0
10100010 01100011 0
10101000 01011000 0
01001111 01010001 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: 1010000111100011
The answer was: 11000
The answer was: 0
The answer was: 13,4
The answer was: No