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 111111001 11010000
10001100 10010101
01111110 10010011
00110100 11111110
10100010 00010000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00010000 00001101 001110100 10000110 1
10011001 01100101 1
01011011 10101001 1
10001010 11000111 0
10101100 10000000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01101110 01111100 000110100 01001000 1
11111110 11100011 1
00101111 11101000 1
01111000 10111010 0
10110011 10010101 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:
11111001 11010000 1
10001100 10010101 1
01111110 10010011 0
00110100 11111110 0
10100010 00010000 0
10011101 00111000 0
1. The parity bits for the 16 columns is: 10011101 00111000
2. The parity bits for the 5 rows is: 11000
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (0,2):
00010000 00001101 0
01110100 10000110 1
10011001 01100101 1
01011011 10101001 1
10001010 11000111 0
10101100 10000000 1
For figure 3, the bits that were flipped are (11,4) and (1,2):
01101110 01111100 0
00110100 01001000 1
11111110 11100011 1
00101111 11101000 1
01111000 10111010 0
10110011 10010101 1
5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.
That's incorrect
That's correct
The answer was: 1001110100111000
The answer was: 11000
The answer was: 0
The answer was: 0,2
The answer was: No