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 101010001 00000001
10011011 00111001
10111101 00101011
10110101 10011010
01111100 11101010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00001110 01100011 101110101 01101001 1
10111000 10011111 0
11011011 10100011 0
10011001 00101001 1
00000001 00011111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10101000 01011110 011101110 10001110 0
10111010 01101001 1
11110101 11111011 1
01010001 00001101 0
01011000 11001111 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:
01010001 00000001 0
10011011 00111001 1
10111101 00101011 0
10110101 10011010 1
01111100 11101010 0
10111110 01100011 0
1. The parity bits for the 16 columns is: 10111110 01100011
2. The parity bits for the 5 rows is: 01010
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (0,5):
00001110 01100011 1
01110101 01101001 1
10111000 10011111 0
11011011 10100011 0
10011001 00101001 1
00000001 00011111 1
For figure 3, the bit that was flipped is (8,5):
10101000 01011110 0
11101110 10001110 0
10111010 01101001 1
11110101 11111011 1
01010001 00001101 0
01011000 11001111 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: 1011111001100011
The answer was: 01010
The answer was: 0
The answer was: 0,5
The answer was: Yes