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 101001001 11111110
10000111 00011011
10100100 00101100
01111001 11111001
10101110 10000101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11001010 01000100 000011101 11011111 0
11100101 10100101 1
01110110 00110101 1
01000010 00000011 0
00000110 00001100 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10111100 00001101 011011100 01011001 1
11101001 11000111 0
00001001 11101001 0
11011100 10101000 1
11001100 11010010 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:
01001001 11111110 0
10000111 00011011 0
10100100 00101100 0
01111001 11111001 1
10101110 10000101 0
10111101 10110101 1
1. The parity bits for the 16 columns is: 10111101 10110101
2. The parity bits for the 5 rows is: 00010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (13,1):
11001010 01000100 0
00011101 11011111 0
11100101 10100101 1
01110110 00110101 1
01000010 00000011 0
00000110 00001100 0
For figure 3, the bits that were flipped are (3,3) and (0,4):
10111100 00001101 0
11011100 01011001 1
11101001 11000111 0
00001001 11101001 0
11011100 10101000 1
11001100 11010010 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: 1011110110110101
The answer was: 00010
The answer was: 1
The answer was: 13,1
The answer was: No