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 111000011 01010110
11110001 01101100
01100101 11001110
10100011 11101001
11011100 01110111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10011000 00110100 001100110 00001000 1
00110010 11101110 1
10100100 10101011 0
10111000 10101010 1
11000000 11010011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10001101 11101001 101001001 01000011 0
01000010 11010111 0
10101110 10000010 1
11001100 01110100 0
11100100 10000011 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:
11000011 01010110 0
11110001 01101100 1
01100101 11001110 1
10100011 11101001 1
11011100 01110111 1
00101000 01101010 0
1. The parity bits for the 16 columns is: 00101000 01101010
2. The parity bits for the 5 rows is: 01111
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (3,4):
10011000 00110100 0
01100110 00001000 1
00110010 11101110 1
10100100 10101011 0
10111000 10101010 1
11000000 11010011 1
For figure 3, the bit that was flipped is (12,5):
10001101 11101001 1
01001001 01000011 0
01000010 11010111 0
10101110 10000010 1
11001100 01110100 0
11100100 10000011 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0010100001101010
The answer was: 01111
The answer was: 0
The answer was: 3,4
The answer was: Yes