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 100010000 10010011
01011011 10101100
11101100 11000001
10110001 01111010
10101110 11011110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101001 00010110 000111100 10101001 0
11000101 10111110 0
11001110 10010001 0
11101010 11001100 1
11100100 01011100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01010010 00110101 101001000 11011111 1
11001001 01011000 1
10011000 00010100 1
01111110 01101011 1
00100101 11001101 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:
00010000 10010011 1
01011011 10101100 1
11101100 11000001 0
10110001 01111010 1
10101110 11011110 1
10111000 01011010 0
1. The parity bits for the 16 columns is: 10111000 01011010
2. The parity bits for the 5 rows is: 11011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (3,5):
00101001 00010110 0
00111100 10101001 0
11000101 10111110 0
11001110 10010001 0
11101010 11001100 1
11100100 01011100 1
For figure 3, the bit that was flipped is (3,5):
01010010 00110101 1
01001000 11011111 1
11001001 01011000 1
10011000 00010100 1
01111110 01101011 1
00100101 11001101 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: 1011100001011010
The answer was: 11011
The answer was: 0
The answer was: 3,5
The answer was: Yes