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 111000010 00011000
11000110 00000010
01010011 01001101
10101101 10001011
11100101 01101011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10010001 10111001 000100111 00101101 0
11110101 00011011 0
01010010 00000000 1
10100010 00000000 0
10110011 10001110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00101111 00011001 010010011 11010011 1
10001110 01010101 0
11010110 00110001 0
10010001 00110110 1
01100101 10011000 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:
11000010 00011000 1
11000110 00000010 1
01010011 01001101 0
10101101 10001011 1
11100101 01101011 0
00011111 10110111 1
1. The parity bits for the 16 columns is: 00011111 10110111
2. The parity bits for the 5 rows is: 11010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (15,4):
10010001 10111001 0
00100111 00101101 0
11110101 00011011 0
01010010 00000000 1
10100010 00000000 0
10110011 10001110 1
For figure 3, the bit that was flipped is (3,5):
00101111 00011001 0
10010011 11010011 1
10001110 01010101 0
11010110 00110001 0
10010001 00110110 1
01100101 10011000 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: 0001111110110111
The answer was: 11010
The answer was: 1
The answer was: 15,4
The answer was: Yes