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 101100111 11100010
01100000 01111101
01011100 00000111
00010110 00000101
10111100 10011011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10001001 11010100 110001110 11100001 0
00000011 01111000 0
11101000 01010001 1
01001000 10011001 0
10100100 10001101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11111010 00110101 011101100 00010010 1
10001010 01101100 1
00001001 00101011 1
10001111 01001100 1
00011010 10100100 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:
01100111 11100010 1
01100000 01111101 0
01011100 00000111 1
00010110 00000101 1
10111100 10011011 0
11110001 00000110 1
1. The parity bits for the 16 columns is: 11110001 00000110
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 (12,5):
10001001 11010100 1
10001110 11100001 0
00000011 01111000 0
11101000 01010001 1
01001000 10011001 0
10100100 10001101 0
For figure 3, the bits that were flipped are (8,4) and (12,3):
11111010 00110101 0
11101100 00010010 1
10001010 01101100 1
00001001 00101011 1
10001111 01001100 1
00011010 10100100 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: 1111000100000110
The answer was: 10110
The answer was: 1
The answer was: 12,5
The answer was: No