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 110010100 01011110
01011000 11010111
00101100 00111001
10100111 01101110
00101001 00010100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10101001 00110000 000010010 10100111 1
00010101 10011110 0
11001011 01010110 1
10111000 00110010 1
01011101 01101101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01100001 10111111 010100101 10011111 0
01110111 01101000 1
11110111 01111100 1
01110110 01101110 0
00110010 00010010 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:
10010100 01011110 0
01011000 11010111 1
00101100 00111001 1
10100111 01101110 0
00101001 00010100 1
01101110 11001010 1
1. The parity bits for the 16 columns is: 01101110 11001010
2. The parity bits for the 5 rows is: 01101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (0,5):
10101001 00110000 0
00010010 10100111 1
00010101 10011110 0
11001011 01010110 1
10111000 00110010 1
01011101 01101101 1
For figure 3, the bits that were flipped are (12,3) and (9,5):
01100001 10111111 0
10100101 10011111 0
01110111 01101000 1
11110111 01111100 1
01110110 01101110 0
00110010 00010010 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: 0110111011001010
The answer was: 01101
The answer was: 1
The answer was: 0,5
The answer was: No