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 101101000 11101100
01100000 10100010
11110111 10111010
11110011 11001001
11000110 00100101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11111111 01111110 010011010 01101001 0
11001110 01000000 0
11100000 01010100 1
11010111 00000001 1
10011100 00000010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00101010 11101101 001001001 01101001 1
00000011 10010100 1
11000001 00000100 0
01100110 01010101 0
11000101 01000001 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:
01101000 11101100 0
01100000 10100010 1
11110111 10111010 0
11110011 11001001 0
11000110 00100101 1
11001010 00011000 0
1. The parity bits for the 16 columns is: 11001010 00011000
2. The parity bits for the 5 rows is: 01001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (16,3):
11111111 01111110 0
10011010 01101001 0
11001110 01000000 0
11100000 01010100 1
11010111 00000001 1
10011100 00000010 1
For figure 3, the bit that was flipped is (6,0):
00101010 11101101 0
01001001 01101001 1
00000011 10010100 1
11000001 00000100 0
01100110 01010101 0
11000101 01000001 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: 1100101000011000
The answer was: 01001
The answer was: 0
The answer was: 16,3
The answer was: Yes