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 111110011 10111011
10100111 00100111
10000001 11001100
01110011 01110001
00011101 01100101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11111010 00001010 010010110 00001100 0
10010000 01100011 1
10101100 10010110 0
01001101 01011001 0
00011101 10101010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01110111 11000110 000101001 10010101 1
10001101 11010110 1
00000100 11111110 0
01110110 00001001 1
11100001 01110010 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:
11110011 10111011 0
10100111 00100111 1
10000001 11001100 0
01110011 01110001 1
00011101 01100101 0
10111011 01000100 0
1. The parity bits for the 16 columns is: 10111011 01000100
2. The parity bits for the 5 rows is: 01010
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (16,2):
11111010 00001010 0
10010110 00001100 0
10010000 01100011 1
10101100 10010110 0
01001101 01011001 0
00011101 10101010 0
For figure 3, the bit that was flipped is (1,5):
01110111 11000110 0
00101001 10010101 1
10001101 11010110 1
00000100 11111110 0
01110110 00001001 1
11100001 01110010 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: 1011101101000100
The answer was: 01010
The answer was: 0
The answer was: 16,2
The answer was: Yes