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 111001101 00101000
10000000 01001101
00011110 11000111
11110101 11110001
10000100 10101011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10001111 10001000 110111011 10001110 0
01101101 11111001 0
01111100 10110011 0
00001101 00111010 1
10101000 01110110 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00001111 00101001 111001111 01001111 1
10111010 11100010 1
10001000 01011111 1
11011010 10010111 0
00101001 01001100 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:
11001101 00101000 1
10000000 01001101 1
00011110 11000111 1
11110101 11110001 1
10000100 10101011 1
00100010 11111000 1
1. The parity bits for the 16 columns is: 00100010 11111000
2. The parity bits for the 5 rows is: 11111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (0,2):
10001111 10001000 1
10111011 10001110 0
01101101 11111001 0
01111100 10110011 0
00001101 00111010 1
10101000 01110110 0
For figure 3, the bit that was flipped is (7,3):
00001111 00101001 1
11001111 01001111 1
10111010 11100010 1
10001000 01011111 1
11011010 10010111 0
00101001 01001100 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: 0010001011111000
The answer was: 11111
The answer was: 1
The answer was: 0,2
The answer was: Yes