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 111100000 00001001
11101110 00101000
01111101 10111110
01001101 11010111
01011100 10000100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00010101 00011111 011001000 00101010 0
10110011 00100101 0
00011111 10110000 1
10100111 11101110 1
11010110 01001010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10000111 11001000 110011000 10111111 0
11111011 10011000 0
11110110 01101010 1
01111001 00010001 1
11101011 10010100 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:
11100000 00001001 1
11101110 00101000 0
01111101 10111110 0
01001101 11010111 0
01011100 10000100 0
01100010 11001100 1
1. The parity bits for the 16 columns is: 01100010 11001100
2. The parity bits for the 5 rows is: 10000
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (13,3):
00010101 00011111 0
11001000 00101010 0
10110011 00100101 0
00011111 10110000 1
10100111 11101110 1
11010110 01001010 0
For figure 3, the bit that was flipped is (0,3):
10000111 11001000 1
10011000 10111111 0
11111011 10011000 0
11110110 01101010 1
01111001 00010001 1
11101011 10010100 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: 0110001011001100
The answer was: 10000
The answer was: 1
The answer was: 13,3
The answer was: Yes