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 100111111 01100000
00000000 01010011
11001000 01111100
11001111 01111011
01101100 10110111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00010100 11000100 101100100 01100000 1
01110110 00000001 1
11100110 11011000 1
10011011 00001010 1
01111011 01110110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00101101 01000000 100110001 11100101 0
00110001 10011011 0
01101100 10110000 0
11111111 01001001 1
10101110 11000111 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:
00111111 01100000 0
00000000 01010011 0
11001000 01111100 0
11001111 01111011 0
01101100 10110111 0
01010100 10000011 0
1. The parity bits for the 16 columns is: 01010100 10000011
2. The parity bits for the 5 rows is: 00000
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (15,2):
00010100 11000100 1
01100100 01100000 1
01110110 00000001 1
11100110 11011000 1
10011011 00001010 1
01111011 01110110 1
For figure 3, the bit that was flipped is (3,3):
00101101 01000000 1
00110001 11100101 0
00110001 10011011 0
01101100 10110000 0
11111111 01001001 1
10101110 11000111 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: 0101010010000011
The answer was: 00000
The answer was: 0
The answer was: 15,2
The answer was: Yes