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 110100100 11010110
10010011 00111101
01101000 00100000
10001010 00011111
01100101 00110011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01010001 11110000 111101111 10010011 1
01011101 01000001 1
01110010 00000011 0
00001101 00011010 0
10011110 00111011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01000110 01110111 111100101 10101011 1
01000100 00000000 0
00010101 11001111 1
11011010 11111100 1
00101100 11101111 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:
10100100 11010110 0
10010011 00111101 1
01101000 00100000 0
10001010 00011111 0
01100101 00110011 0
10110000 11100111 1
1. The parity bits for the 16 columns is: 10110000 11100111
2. The parity bits for the 5 rows is: 01000
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (6,5):
01010001 11110000 1
11101111 10010011 1
01011101 01000001 1
01110010 00000011 0
00001101 00011010 0
10011110 00111011 1
For figure 3, the bit that was flipped is (5,1):
01000110 01110111 1
11100101 10101011 1
01000100 00000000 0
00010101 11001111 1
11011010 11111100 1
00101100 11101111 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: 1011000011100111
The answer was: 01000
The answer was: 1
The answer was: 6,5
The answer was: Yes