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 111000111 01101000
11001011 11011010
01101101 01010000
00101101 00010011
00111110 00111100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11111110 10111011 101010010 10110101 0
00001100 11110101 0
11111111 01100010 0
10110111 00011010 1
01101000 10000011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01110100 11101000 000100100 00111010 0
01110101 10010010 1
10101100 11010010 1
10010111 11110100 0
00010110 01000110 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:
11000111 01101000 0
11001011 11011010 0
01101101 01010000 1
00101101 00010011 1
00111110 00111100 1
01110010 11001101 1
1. The parity bits for the 16 columns is: 01110010 11001101
2. The parity bits for the 5 rows is: 00111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (0,3):
11111110 10111011 1
01010010 10110101 0
00001100 11110101 0
11111111 01100010 0
10110111 00011010 1
01101000 10000011 0
For figure 3, the bits that were flipped are (4,3) and (10,2):
01110100 11101000 0
00100100 00111010 0
01110101 10010010 1
10101100 11010010 1
10010111 11110100 0
00010110 01000110 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: 0111001011001101
The answer was: 00111
The answer was: 1
The answer was: 0,3
The answer was: No