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 101111100 00110111
00100000 00101110
01100110 10111000
11100011 11011110
10100011 10010100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00011100 01100011 100100100 11111100 0
11001111 00111011 1
01100010 00110001 0
00011011 00001111 0
10101110 10011010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00001100 00001000 000010100 00011100 1
10100101 10011101 0
10011011 00101011 1
00111101 11000001 0
00110011 01100011 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:
01111100 00110111 0
00100000 00101110 1
01100110 10111000 0
11100011 11011110 1
10100011 10010100 1
01111010 11101011 1
1. The parity bits for the 16 columns is: 01111010 11101011
2. The parity bits for the 5 rows is: 01011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (2,5):
00011100 01100011 1
00100100 11111100 0
11001111 00111011 1
01100010 00110001 0
00011011 00001111 0
10101110 10011010 0
For figure 3, the bits that were flipped are (4,2) and (2,0):
00001100 00001000 0
00010100 00011100 1
10100101 10011101 0
10011011 00101011 1
00111101 11000001 0
00110011 01100011 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: 0111101011101011
The answer was: 01011
The answer was: 1
The answer was: 2,5
The answer was: No