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 101000011 11000010
01001100 10010111
10111011 00110010
11001001 00010110
01011000 01100001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10000100 10101101 101000111 10001001 1
11001010 10101101 1
11001100 10001110 0
10010101 00001010 0
01010001 00001101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10000010 11100010 000011100 00101100 1
01011100 11010111 0
11000000 11001111 0
11111110 01011100 1
11111000 10001010 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:
01000011 11000010 0
01001100 10010111 0
10111011 00110010 1
11001001 00010110 1
01011000 01100001 0
00100101 00010000 0
1. The parity bits for the 16 columns is: 00100101 00010000
2. The parity bits for the 5 rows is: 00110
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (7,5):
10000100 10101101 1
01000111 10001001 1
11001010 10101101 1
11001100 10001110 0
10010101 00001010 0
01010001 00001101 1
For figure 3, the bit that was flipped is (5,1):
10000010 11100010 0
00011100 00101100 1
01011100 11010111 0
11000000 11001111 0
11111110 01011100 1
11111000 10001010 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: 0010010100010000
The answer was: 00110
The answer was: 0
The answer was: 7,5
The answer was: Yes