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 100000101 11001000
10011011 10111010
01010010 11110001
11101011 01011001
01001000 11001100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00010001 00001011 010110000 11000011 1
01101101 10101100 1
10100110 01001111 1
00011001 11001011 0
01110011 11000000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00000110 00010001 000010000 11001110 1
00100010 00000001 1
00001000 00100010 1
10011001 11111101 1
10100101 00000111 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:
00000101 11001000 1
10011011 10111010 0
01010010 11110001 0
11101011 01011001 0
01001000 11001100 0
01101111 00010110 1
1. The parity bits for the 16 columns is: 01101111 00010110
2. The parity bits for the 5 rows is: 10000
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (10,0):
00010001 00001011 0
10110000 11000011 1
01101101 10101100 1
10100110 01001111 1
00011001 11001011 0
01110011 11000000 1
For figure 3, the bits that were flipped are (14,1) and (13,5):
00000110 00010001 0
00010000 11001110 1
00100010 00000001 1
00001000 00100010 1
10011001 11111101 1
10100101 00000111 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: 0110111100010110
The answer was: 10000
The answer was: 1
The answer was: 10,0
The answer was: No