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 100101111 10010110
10101110 00010100
11101100 11000101
10001010 01101011
10011011 10001011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10100100 10110111 111000000 11000011 1
01010000 11111000 1
10010110 01010010 1
00001000 10110010 1
10100010 01101100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10100110 01011100 000101000 10001011 0
01100101 01001001 0
01011011 00001001 1
01011111 00101110 0
11101111 11111001 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:
00101111 10010110 1
10101110 00010100 1
11101100 11000101 1
10001010 01101011 0
10011011 10001011 1
01111100 10100111 0
1. The parity bits for the 16 columns is: 01111100 10100111
2. The parity bits for the 5 rows is: 11101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (4,1):
10100100 10110111 1
11000000 11000011 1
01010000 11111000 1
10010110 01010010 1
00001000 10110010 1
10100010 01101100 1
For figure 3, the bit that was flipped is (9,2):
10100110 01011100 0
00101000 10001011 0
01100101 01001001 0
01011011 00001001 1
01011111 00101110 0
11101111 11111001 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: 0111110010100111
The answer was: 11101
The answer was: 0
The answer was: 4,1
The answer was: Yes