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 110100111 00000010
11111101 00111110
01010111 00011110
11001101 10000111
01000101 11001111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01001100 00110100 001001001 11000100 0
10001000 01001010 1
01000011 01110010 1
10110001 00001110 1
01111111 11000010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01101001 11000011 100101001 01110101 0
11010010 10000001 0
10100000 00101111 1
10111110 10000001 0
10001110 10111001 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:
10100111 00000010 0
11111101 00111110 0
01010111 00011110 1
11001101 10000111 1
01000101 11001111 1
10000101 01101010 1
1. The parity bits for the 16 columns is: 10000101 01101010
2. The parity bits for the 5 rows is: 00111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (13,5):
01001100 00110100 0
01001001 11000100 0
10001000 01001010 1
01000011 01110010 1
10110001 00001110 1
01111111 11000010 1
For figure 3, the bits that were flipped are (10,5) and (6,0):
01101001 11000011 1
00101001 01110101 0
11010010 10000001 0
10100000 00101111 1
10111110 10000001 0
10001110 10111001 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: 1000010101101010
The answer was: 00111
The answer was: 1
The answer was: 13,5
The answer was: No