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 110000101 00101000
01010010 11010110
00011111 01001010
01101010 00110100
11011001 10001111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110101 01011011 110101011 01000100 1
11000000 00001111 1
00000010 11011011 1
00100101 11010111 1
11111001 00011100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01000110 01011000 011000010 00110010 0
00010000 10011011 0
00000000 11111111 0
00010010 00000011 1
10001110 00001101 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:
10000101 00101000 1
01010010 11010110 0
00011111 01001010 0
01101010 00110100 1
11011001 10001111 0
01111011 00001111 0
1. The parity bits for the 16 columns is: 01111011 00001111
2. The parity bits for the 5 rows is: 10010
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (1,2):
11110101 01011011 1
10101011 01000100 1
11000000 00001111 1
00000010 11011011 1
00100101 11010111 1
11111001 00011100 1
For figure 3, the bit that was flipped is (4,4):
01000110 01011000 0
11000010 00110010 0
00010000 10011011 0
00000000 11111111 0
00010010 00000011 1
10001110 00001101 1
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0111101100001111
The answer was: 10010
The answer was: 0
The answer was: 1,2
The answer was: Yes