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 111111010 01001101
01101110 11110001
11010100 11101011
10000101 10011000
01001110 01111001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10001110 00000110 000000100 10101000 0
10101101 10011011 0
11111101 11000000 0
00000101 01110000 1
11011110 10000101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11111001 00000001 100010001 10010101 0
10011111 01011111 1
11101011 10001100 0
10100011 11000100 1
00101101 10000011 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:
11111010 01001101 0
01101110 11110001 0
11010100 11101011 0
10000101 10011000 0
01001110 01111001 1
10001011 10110110 1
1. The parity bits for the 16 columns is: 10001011 10110110
2. The parity bits for the 5 rows is: 00001
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (7,3):
10001110 00000110 0
00000100 10101000 0
10101101 10011011 0
11111101 11000000 0
00000101 01110000 1
11011110 10000101 1
For figure 3, the bits that were flipped are (3,2) and (6,3):
11111001 00000001 1
00010001 10010101 0
10011111 01011111 1
11101011 10001100 0
10100011 11000100 1
00101101 10000011 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: 1000101110110110
The answer was: 00001
The answer was: 1
The answer was: 7,3
The answer was: No