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 110101010 11011111
01101101 10111001
11100101 11001110
01010101 10011100
10011100 01111100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10101000 10110010 111010111 00001101 1
00011110 00110011 0
11001011 00000111 0
10100000 01100001 1
00001010 11100010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11100001 00011000 000010111 01010011 1
01011110 11011111 0
10111010 11010110 0
11111010 00010100 0
11101000 00010110 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:
10101010 11011111 1
01101101 10111001 0
11100101 11001110 0
01010101 10011100 0
10011100 01111100 1
11101011 01001000 0
1. The parity bits for the 16 columns is: 11101011 01001000
2. The parity bits for the 5 rows is: 10001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (12,5):
10101000 10110010 1
11010111 00001101 1
00011110 00110011 0
11001011 00000111 0
10100000 01100001 1
00001010 11100010 1
For figure 3, the bit that was flipped is (9,1):
11100001 00011000 0
00010111 01010011 1
01011110 11011111 0
10111010 11010110 0
11111010 00010100 0
11101000 00010110 1
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 1110101101001000
The answer was: 10001
The answer was: 0
The answer was: 12,5
The answer was: Yes