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 10111100
11011010 00000111
11000101 10011110
00100010 01101010
11001001 00000100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10110110 01000110 001101011 11011110 1
01010001 11100111 0
01011110 00110011 1
00101100 10010101 1
11111110 11001001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01100000 01010110 110100111 11001100 1
01010101 01000011 1
10010000 10010101 0
00100000 11010000 0
00001010 10011100 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 10111100 1
11011010 00000111 0
11000101 10011110 1
00100010 01101010 0
11001001 00000100 1
00001110 01001011 1
1. The parity bits for the 16 columns is: 00001110 01001011
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 (11,2):
10110110 01000110 0
01101011 11011110 1
01010001 11100111 0
01011110 00110011 1
00101100 10010101 1
11111110 11001001 1
For figure 3, the bits that were flipped are (2,0) and (4,5):
01100000 01010110 1
10100111 11001100 1
01010101 01000011 1
10010000 10010101 0
00100000 11010000 0
00001010 10011100 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: 0000111001001011
The answer was: 10101
The answer was: 1
The answer was: 11,2
The answer was: No