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 111101000 00111101
10100000 00011100
00101000 00000001
10101011 10011001
10011101 11110011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10011000 00011010 000101100 11011010 1
00110101 00100010 0
10101110 00100001 1
01001010 10111001 0
00100101 01111010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01010101 00001010 101001110 00011101 0
00101101 01011001 0
01100111 11110110 1
00010010 01001010 1
01000010 10110010 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:
11101000 00111101 1
10100000 00011100 1
00101000 00000001 1
10101011 10011001 1
10011101 11110011 1
01010110 01001010 1
1. The parity bits for the 16 columns is: 01010110 01001010
2. The parity bits for the 5 rows is: 11111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (1,1):
10011000 00011010 0
00101100 11011010 1
00110101 00100010 0
10101110 00100001 1
01001010 10111001 0
00100101 01111010 0
For figure 3, the bits that were flipped are (9,5) and (7,0):
01010101 00001010 1
01001110 00011101 0
00101101 01011001 0
01100111 11110110 1
00010010 01001010 1
01000010 10110010 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: 0101011001001010
The answer was: 11111
The answer was: 1
The answer was: 1,1
The answer was: No