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 100100110 01100001
01011010 00101010
10001000 00010100
00111100 00011010
00111000 01000011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10011100 01001110 001110111 10001110 0
00100110 01011110 1
00010110 00100000 0
10110001 11011101 0
01101010 01110011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01000010 10100001 110110110 11011101 1
11100111 01100010 1
01010010 00010100 0
01101111 01000001 0
10101110 01101011 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:
00100110 01100001 0
01011010 00101010 1
10001000 00010100 0
00111100 00011010 1
00111000 01000011 0
11110000 00000110 0
1. The parity bits for the 16 columns is: 11110000 00000110
2. The parity bits for the 5 rows is: 01010
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (11,2):
10011100 01001110 0
01110111 10001110 0
00100110 01011110 1
00010110 00100000 0
10110001 11011101 0
01101010 01110011 1
For figure 3, the bits that were flipped are (0,5) and (10,3):
01000010 10100001 1
10110110 11011101 1
11100111 01100010 1
01010010 00010100 0
01101111 01000001 0
10101110 01101011 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: 1111000000000110
The answer was: 01010
The answer was: 0
The answer was: 11,2
The answer was: No