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 110101100 10101000
10100100 01101100
01100100 01110010
01001000 10000011
01001111 01000100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110111 10000111 100010111 11100110 0
00001110 01100110 1
01000011 10101001 1
00111011 00001011 0
11010110 10100101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11000100 10010111 010001100 01111111 0
10010100 01010110 1
11111011 01111000 0
00011101 10110110 0
00111110 01110001 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:
10101100 10101000 1
10100100 01101100 1
01100100 01110010 1
01001000 10000011 1
01001111 01000100 1
01101011 01110001 1
1. The parity bits for the 16 columns is: 01101011 01110001
2. The parity bits for the 5 rows is: 11111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (1,1):
11110111 10000111 1
00010111 11100110 0
00001110 01100110 1
01000011 10101001 1
00111011 00001011 0
11010110 10100101 1
For figure 3, the bits that were flipped are (5,4) and (15,3):
11000100 10010111 0
10001100 01111111 0
10010100 01010110 1
11111011 01111000 0
00011101 10110110 0
00111110 01110001 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: 0110101101110001
The answer was: 11111
The answer was: 1
The answer was: 1,1
The answer was: No