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 110111011 11100000
10101111 01011101
01000111 00000000
10101110 01110100
11111001 00010010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11011001 01110111 100001111 11011100 1
11000000 00110000 0
11100110 01111011 0
01011111 11101101 0
10101011 00001101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01000001 11001001 011101001 00010100 1
00100000 01110110 1
01111011 10100010 1
00011000 00000110 0
11101001 00001111 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:
10111011 11100000 1
10101111 01011101 1
01000111 00000000 0
10101110 01110100 1
11111001 00010010 0
00000100 11011011 1
1. The parity bits for the 16 columns is: 00000100 11011011
2. The parity bits for the 5 rows is: 11010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (5,3):
11011001 01110111 1
00001111 11011100 1
11000000 00110000 0
11100110 01111011 0
01011111 11101101 0
10101011 00001101 0
For figure 3, the bit that was flipped is (6,2):
01000001 11001001 0
11101001 00010100 1
00100000 01110110 1
01111011 10100010 1
00011000 00000110 0
11101001 00001111 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: 0000010011011011
The answer was: 11010
The answer was: 1
The answer was: 5,3
The answer was: Yes