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 111011010 11010101
00001111 11010010
11000000 01010110
11110001 00110110
11001100 10100110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110011 00100001 001100110 00100010 0
10111000 00011001 1
01001111 11011100 1
11100101 00100011 0
11000111 11100101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00101100 01111110 100000000 01100001 1
01111010 11100011 0
10110110 00111011 1
00000110 01110111 0
11100110 10100000 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:
11011010 11010101 0
00001111 11010010 0
11000000 01010110 0
11110001 00110110 1
11001100 10100110 0
00101000 11000001 1
1. The parity bits for the 16 columns is: 00101000 11000001
2. The parity bits for the 5 rows is: 00010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (1,3):
11110011 00100001 0
01100110 00100010 0
10111000 00011001 1
01001111 11011100 1
11100101 00100011 0
11000111 11100101 0
For figure 3, the bit that was flipped is (11,3):
00101100 01111110 1
00000000 01100001 1
01111010 11100011 0
10110110 00111011 1
00000110 01110111 0
11100110 10100000 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: 0010100011000001
The answer was: 00010
The answer was: 1
The answer was: 1,3
The answer was: Yes