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 110010101 01100110
11011010 01111101
10110100 11010110
11101000 10110101
10000001 01100101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00111100 10001000 000011000 01111101 1
10101101 01111001 0
11001010 01101110 1
00010111 01010100 1
01010100 10010110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01100111 01011000 110111110 01100000 0
11001111 11100110 1
00100001 11100111 0
11101110 10110100 0
01011001 10001101 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:
10010101 01100110 0
11011010 01111101 1
10110100 11010110 1
11101000 10110101 1
10000001 01100101 0
10010010 00011101 1
1. The parity bits for the 16 columns is: 10010010 00011101
2. The parity bits for the 5 rows is: 01110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (10,1):
00111100 10001000 0
00011000 01111101 1
10101101 01111001 0
11001010 01101110 1
00010111 01010100 1
01010100 10010110 1
For figure 3, the bit that was flipped is (0,0):
01100111 01011000 1
10111110 01100000 0
11001111 11100110 1
00100001 11100111 0
11101110 10110100 0
01011001 10001101 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: 1001001000011101
The answer was: 01110
The answer was: 1
The answer was: 10,1
The answer was: Yes