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 100010100 10111100
11101101 01110001
10011001 01000000
00100100 10010011
01100100 11011110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101011 01001110 011011011 10110010 0
01001101 01010001 1
00111110 11000010 1
01101101 01101111 1
11101010 00000000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11001011 01010101 100100111 10111001 1
11001100 01010011 1
11010110 11000110 1
00101000 10011111 0
11011110 10100010 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:
00010100 10111100 1
11101101 01110001 0
10011001 01000000 1
00100100 10010011 0
01100100 11011110 1
00100000 11000000 1
1. The parity bits for the 16 columns is: 00100000 11000000
2. The parity bits for the 5 rows is: 10101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (5,3):
00101011 01001110 0
11011011 10110010 0
01001101 01010001 1
00111110 11000010 1
01101101 01101111 1
11101010 00000000 1
For figure 3, the bits that were flipped are (9,5) and (13,2):
11001011 01010101 1
00100111 10111001 1
11001100 01010011 1
11010110 11000110 1
00101000 10011111 0
11011110 10100010 0
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: 0010000011000000
The answer was: 10101
The answer was: 1
The answer was: 5,3
The answer was: No