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 110010000 00001100
11000011 00001110
01101011 11010001
11100101 01011001
01101100 00010000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110010 11111001 111011111 01111010 1
01001110 01001101 0
10111100 10011111 1
01001111 01010111 0
00010000 00000110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00011001 00101111 010011001 11000110 0
01101000 11100101 0
11001011 11101001 0
11100011 01000001 0
11100000 10100100 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:
10010000 00001100 0
11000011 00001110 1
01101011 11010001 1
11100101 01011001 1
01101100 00010000 1
10110001 10011010 0
1. The parity bits for the 16 columns is: 10110001 10011010
2. The parity bits for the 5 rows is: 01111
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (0,1):
11110010 11111001 1
11011111 01111010 1
01001110 01001101 0
10111100 10011111 1
01001111 01010111 0
00010000 00000110 1
For figure 3, the bit that was flipped is (2,4):
00011001 00101111 0
10011001 11000110 0
01101000 11100101 0
11001011 11101001 0
11100011 01000001 0
11100000 10100100 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: 1011000110011010
The answer was: 01111
The answer was: 0
The answer was: 0,1
The answer was: Yes