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 111000010 01011110
01110001 10111000
01011000 11101000
11100110 11110101
10110100 00110111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00111010 00111011 101011011 11110001 0
10100100 01111111 1
00001000 10101101 0
10111111 01001101 1
01110010 00010101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01011100 11110001 001011100 11001010 0
11111001 10100111 1
10110101 10010011 1
01110100 11000100 1
00111001 11001011 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:
11000010 01011110 0
01110001 10111000 0
01011000 11101000 1
11100110 11110101 1
10110100 00110111 1
10111001 11001100 1
1. The parity bits for the 16 columns is: 10111001 11001100
2. The parity bits for the 5 rows is: 00111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (9,2):
00111010 00111011 1
01011011 11110001 0
10100100 01111111 1
00001000 10101101 0
10111111 01001101 1
01110010 00010101 1
For figure 3, the bit that was flipped is (7,0):
01011100 11110001 0
01011100 11001010 0
11111001 10100111 1
10110101 10010011 1
01110100 11000100 1
00111001 11001011 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: 1011100111001100
The answer was: 00111
The answer was: 1
The answer was: 9,2
The answer was: Yes