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 100010011 00110011
01111111 01101111
11011011 00100000
01001010 10110011
10000000 00101001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10010101 00100001 001001110 10101011 1
10010011 01011100 0
01010001 01001011 0
01011101 00100101 0
11000100 10111000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00100100 00111001 010101100 01001111 1
10110101 00110001 0
01010001 00001110 1
10100111 11010110 0
11001011 00011111 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:
00010011 00110011 1
01111111 01101111 1
11011011 00100000 1
01001010 10110011 0
10000000 00101001 0
01111101 11100110 1
1. The parity bits for the 16 columns is: 01111101 11100110
2. The parity bits for the 5 rows is: 11100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (0,3):
10010101 00100001 0
01001110 10101011 1
10010011 01011100 0
01010001 01001011 0
01011101 00100101 0
11000100 10111000 1
For figure 3, the bit that was flipped is (8,3):
00100100 00111001 0
10101100 01001111 1
10110101 00110001 0
01010001 00001110 1
10100111 11010110 0
11001011 00011111 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0111110111100110
The answer was: 11100
The answer was: 1
The answer was: 0,3
The answer was: Yes