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 110001010 00000010
11111110 11011011
00011101 01000110
11101110 11001110
00100101 10010010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10110010 01011011 011111011 01101111 1
10111010 11111100 1
10010100 00001010 1
00000010 00111010 1
01100101 11101000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00100011 10011001 110010001 10101010 1
00110111 11111001 1
00110000 01111101 0
01001100 10001110 1
11111001 00011001 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:
10001010 00000010 0
11111110 11011011 1
00011101 01000110 1
11101110 11001110 1
00100101 10010010 0
10100010 11000011 1
1. The parity bits for the 16 columns is: 10100010 11000011
2. The parity bits for the 5 rows is: 01110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (11,0):
10110010 01011011 0
11111011 01101111 1
10111010 11111100 1
10010100 00001010 1
00000010 00111010 1
01100101 11101000 0
For figure 3, the bit that was flipped is (10,5):
00100011 10011001 1
10010001 10101010 1
00110111 11111001 1
00110000 01111101 0
01001100 10001110 1
11111001 00011001 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: 1010001011000011
The answer was: 01110
The answer was: 1
The answer was: 11,0
The answer was: Yes