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 101101001 11111000
00001010 10101101
00100000 11101111
10001010 11001010
00001001 01100110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01110001 00010010 100101111 11100011 0
01010001 00111100 1
01000011 10011101 0
01000010 11011010 1
00001110 10011010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10011011 10111100 000001011 01100101 1
11110010 01110011 0
01000010 11111100 1
11000000 01001110 1
11100000 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:
01101001 11111000 1
00001010 10101101 1
00100000 11101111 0
10001010 11001010 1
00001001 01100110 0
11000000 00010110 1
1. The parity bits for the 16 columns is: 11000000 00010110
2. The parity bits for the 5 rows is: 11010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (11,0):
01110001 00010010 1
00101111 11100011 0
01010001 00111100 1
01000011 10011101 0
01000010 11011010 1
00001110 10011010 1
For figure 3, the bits that were flipped are (13,3) and (8,4):
10011011 10111100 0
00001011 01100101 1
11110010 01110011 0
01000010 11111100 1
11000000 01001110 1
11100000 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: 1100000000010110
The answer was: 11010
The answer was: 1
The answer was: 11,0
The answer was: No