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 101101110 11001001
11011010 00110010
00001100 01011110
01010101 10011011
01111101 11111111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01101010 01011101 100001010 10001110 1
01011001 00011010 1
01011100 11111101 1
10010011 01000000 1
11110110 00110100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01100111 01100110 110101011 11110111 0
00100111 10111111 1
00111010 00100000 0
01101000 10110111 1
10111000 10111001 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:
01101110 11001001 1
11011010 00110010 0
00001100 01011110 1
01010101 10011011 1
01111101 11111111 0
10010000 11000001 1
1. The parity bits for the 16 columns is: 10010000 11000001
2. The parity bits for the 5 rows is: 10110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (9,1):
01101010 01011101 1
00001010 10001110 1
01011001 00011010 1
01011100 11111101 1
10010011 01000000 1
11110110 00110100 1
For figure 3, the bit that was flipped is (7,3):
01100111 01100110 1
10101011 11110111 0
00100111 10111111 1
00111010 00100000 0
01101000 10110111 1
10111000 10111001 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: 1001000011000001
The answer was: 10110
The answer was: 1
The answer was: 9,1
The answer was: Yes