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 111101001 00011111
01100110 01011000
11111111 11110001
11101001 01101011
11010000 10100110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10001010 11111110 000100000 10110111 1
10001101 00101000 1
10101101 10011110 0
10001101 00010011 1
10000111 11101100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11101100 10111000 101010101 00101010 1
00110000 01100000 0
00000000 00101101 0
10111110 01110011 1
00110111 10101000 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:
11101001 00011111 0
01100110 01011000 1
11111111 11110001 1
11101001 01101011 0
11010000 10100110 1
01001001 01111011 1
1. The parity bits for the 16 columns is: 01001001 01111011
2. The parity bits for the 5 rows is: 01101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (0,2):
10001010 11111110 0
00100000 10110111 1
10001101 00101000 1
10101101 10011110 0
10001101 00010011 1
10000111 11101100 1
For figure 3, the bit that was flipped is (13,5):
11101100 10111000 1
01010101 00101010 1
00110000 01100000 0
00000000 00101101 0
10111110 01110011 1
00110111 10101000 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: 0100100101111011
The answer was: 01101
The answer was: 1
The answer was: 0,2
The answer was: Yes