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 101111011 01100111
11101011 01000000
10111001 01000010
11001100 11000110
10111110 01101011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01101100 01010101 011011001 11111011 0
00100100 10110001 1
00000010 01011100 1
01110011 11011011 1
11100001 10011000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11011111 10110000 010101111 00000111 1
00010000 00101010 1
00010101 01010100 1
10000011 01110001 1
10010110 10111000 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:
01111011 01100111 1
11101011 01000000 1
10111001 01000010 1
11001100 11000110 0
10111110 01101011 1
01011011 11001000 0
1. The parity bits for the 16 columns is: 01011011 11001000
2. The parity bits for the 5 rows is: 11101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (7,2):
01101100 01010101 0
11011001 11111011 0
00100100 10110001 1
00000010 01011100 1
01110011 11011011 1
11100001 10011000 1
For figure 3, the bits that were flipped are (1,3) and (2,2):
11011111 10110000 0
10101111 00000111 1
00010000 00101010 1
00010101 01010100 1
10000011 01110001 1
10010110 10111000 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: 0101101111001000
The answer was: 11101
The answer was: 0
The answer was: 7,2
The answer was: No