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 111001011 00000000
10011101 11001101
01000000 01001111
01010110 10101000
10101101 10111110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10001111 11100001 101100000 01111111 1
01110101 01001111 0
00011001 00000000 0
11111001 11011011 0
01111000 00001010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00010010 11001001 010101001 11100001 0
00111000 11001100 0
00010011 10100001 0
10010110 11111000 1
00000110 10111111 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:
11001011 00000000 1
10011101 11001101 0
01000000 01001111 0
01010110 10101000 1
10101101 10111110 1
11101101 10010100 1
1. The parity bits for the 16 columns is: 11101101 10010100
2. The parity bits for the 5 rows is: 10011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (6,3):
10001111 11100001 1
01100000 01111111 1
01110101 01001111 0
00011001 00000000 0
11111001 11011011 0
01111000 00001010 0
For figure 3, the bit that was flipped is (14,2):
00010010 11001001 0
10101001 11100001 0
00111000 11001100 0
00010011 10100001 0
10010110 11111000 1
00000110 10111111 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: 1110110110010100
The answer was: 10011
The answer was: 1
The answer was: 6,3
The answer was: Yes