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 110000011 10010110
11111100 10011100
01110000 00010101
00011010 10111011
01001001 01110000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01001101 11000011 011101000 01100100 0
11001100 00111010 0
01101000 10001001 0
11110010 01111100 0
11110011 01101010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11100010 11100110 001001000 00110011 0
10011011 10101001 1
01000110 00101100 1
11011100 11000111 0
10101011 10110110 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:
10000011 10010110 1
11111100 10011100 0
01110000 00010101 0
00011010 10111011 1
01001001 01110000 0
01011100 11010100 0
1. The parity bits for the 16 columns is: 01011100 11010100
2. The parity bits for the 5 rows is: 10010
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (14,1):
01001101 11000011 0
11101000 01100100 0
11001100 00111010 0
01101000 10001001 0
11110010 01111100 0
11110011 01101010 0
For figure 3, the bits that were flipped are (10,3) and (15,0):
11100010 11100110 0
01001000 00110011 0
10011011 10101001 1
01000110 00101100 1
11011100 11000111 0
10101011 10110110 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: 0101110011010100
The answer was: 10010
The answer was: 0
The answer was: 14,1
The answer was: No