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 111010101 10010110
10001011 10111110
01000100 01011110
11101010 10001100
10000010 11101000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10000100 00001001 001101011 00110011 0
10000001 00001111 0
11001111 00010111 0
11101011 10001100 1
01101010 10101110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01001100 11000011 100000011 10010100 0
10100001 11111001 0
00110000 11011011 0
11110110 10100011 0
01101000 11000110 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:
11010101 10010110 1
10001011 10111110 0
01000100 01011110 1
11101010 10001100 0
10000010 11101000 0
01110010 00010010 0
1. The parity bits for the 16 columns is: 01110010 00010010
2. The parity bits for the 5 rows is: 10100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (2,1):
10000100 00001001 0
01101011 00110011 0
10000001 00001111 0
11001111 00010111 0
11101011 10001100 1
01101010 10101110 1
For figure 3, the bits that were flipped are (11,2) and (1,1):
01001100 11000011 1
00000011 10010100 0
10100001 11111001 0
00110000 11011011 0
11110110 10100011 0
01101000 11000110 1
5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.
That's incorrect
That's correct
The answer was: 0111001000010010
The answer was: 10100
The answer was: 0
The answer was: 2,1
The answer was: No