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 111101100 01010010
00001001 10111110
10000101 10001110
11111011 01110001
01101000 01111110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110000 11000100 110100101 00110101 0
10111000 00110110 0
11111100 00011011 0
00010001 11011111 0
00000000 00000001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11110110 01100101 011011111 10101100 1
10111011 10010110 1
11010000 00111111 1
10001000 11111111 0
11000010 10011111 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:
11101100 01010010 0
00001001 10111110 0
10000101 10001110 1
11111011 01110001 1
01101000 01111110 1
11110011 01101101 1
1. The parity bits for the 16 columns is: 11110011 01101101
2. The parity bits for the 5 rows is: 00111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (14,4):
11110000 11000100 1
10100101 00110101 0
10111000 00110110 0
11111100 00011011 0
00010001 11011111 0
00000000 00000001 1
For figure 3, the bit that was flipped is (4,2):
11110110 01100101 0
11011111 10101100 1
10111011 10010110 1
11010000 00111111 1
10001000 11111111 0
11000010 10011111 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: 1111001101101101
The answer was: 00111
The answer was: 1
The answer was: 14,4
The answer was: Yes