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 111010010 11101010
10010100 10100101
11000111 11110000
00100010 01111101
11000000 00101111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11101011 00101000 001101001 01111110 1
00010001 01111001 1
00100101 10110111 1
00000010 11001111 1
10111100 01010111 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11101001 11010100 101001001 11011000 0
11010000 00011011 1
00011001 10001000 1
11000110 01100011 0
10111111 11111100 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:
11010010 11101010 1
10010100 10100101 1
11000111 11110000 1
00100010 01111101 0
11000000 00101111 1
01100011 11101101 0
1. The parity bits for the 16 columns is: 01100011 11101101
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):
11101011 00101000 0
01101001 01111110 1
00010001 01111001 1
00100101 10110111 1
00000010 11001111 1
10111100 01010111 0
For figure 3, the bit that was flipped is (3,1):
11101001 11010100 1
01001001 11011000 0
11010000 00011011 1
00011001 10001000 1
11000110 01100011 0
10111111 11111100 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: 0110001111101101
The answer was: 11101
The answer was: 0
The answer was: 4,1
The answer was: Yes