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 111110010 00011011
01101100 11110011
11100001 01011001
11011110 01101000
01100111 11110000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11111010 10000111 100010011 10001100 0
10101011 11010000 0
10010000 00110101 0
10010110 00001111 0
01000100 11101001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10001110 10111101 001000100 01011011 1
00111011 01101001 1
11110001 00001010 1
01110101 00011101 1
01110101 10111000 0
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:
11110010 00011011 1
01101100 11110011 0
11100001 01011001 0
11011110 01101000 1
01100111 11110000 1
11000110 00101001 1
1. The parity bits for the 16 columns is: 11000110 00101001
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 (12,0):
11111010 10000111 1
00010011 10001100 0
10101011 11010000 0
10010000 00110101 0
10010110 00001111 0
01000100 11101001 1
For figure 3, the bit that was flipped is (10,5):
10001110 10111101 0
01000100 01011011 1
00111011 01101001 1
11110001 00001010 1
01110101 00011101 1
01110101 10111000 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 1100011000101001
The answer was: 10011
The answer was: 1
The answer was: 12,0
The answer was: Yes