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 110011100 10011011
00001100 10000100
00101110 00010001
00001100 01110000
11100110 01010110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11100010 11011000 000001101 10000100 0
01001001 11111101 0
10100101 01001111 1
11100010 01011101 1
10100001 10110011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10101101 00110001 101111011 01111100 1
11011010 10010111 0
01001100 11111010 1
11110111 10111111 0
10110111 00011110 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:
10011100 10011011 1
00001100 10000100 0
00101110 00010001 0
00001100 01110000 1
11100110 01010110 1
01010100 00101000 1
1. The parity bits for the 16 columns is: 01010100 00101000
2. The parity bits for the 5 rows is: 10011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (1,1):
11100010 11011000 0
00001101 10000100 0
01001001 11111101 0
10100101 01001111 1
11100010 01011101 1
10100001 10110011 0
For figure 3, the bits that were flipped are (8,5) and (15,0):
10101101 00110001 1
01111011 01111100 1
11011010 10010111 0
01001100 11111010 1
11110111 10111111 0
10110111 00011110 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: 0101010000101000
The answer was: 10011
The answer was: 1
The answer was: 1,1
The answer was: No