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 110101111 01101010
10010111 11011110
11100001 00111100
01001001 10100001
01000110 00010101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10101000 11100000 011110011 10111000 0
11100001 01001010 1
10100101 10011011 1
10111000 01000010 0
10100111 01001011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11010110 01010010 001100111 11110000 0
00110001 00000011 1
01110110 11010100 1
00000100 11110001 1
11110010 00000101 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:
10101111 01101010 0
10010111 11011110 1
11100001 00111100 0
01001001 10100001 0
01000110 00010101 0
11010110 00111100 1
1. The parity bits for the 16 columns is: 11010110 00111100
2. The parity bits for the 5 rows is: 01000
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (8,5):
10101000 11100000 0
11110011 10111000 0
11100001 01001010 1
10100101 10011011 1
10111000 01000010 0
10100111 01001011 0
For figure 3, the bits that were flipped are (8,1) and (15,4):
11010110 01010010 0
01100111 11110000 0
00110001 00000011 1
01110110 11010100 1
00000100 11110001 1
11110010 00000101 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: 1101011000111100
The answer was: 01000
The answer was: 1
The answer was: 8,5
The answer was: No