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 101100011 11111101
00011100 11000000
01001110 01101000
10111001 10011110
11100111 01000100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10110010 11101100 100001001 11110111 1
01111100 01001110 1
10101011 01001001 0
10101011 00000111 1
11000111 10011011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11000100 01011110 000110100 00100000 0
10101100 11101011 1
00110001 01110011 0
00010011 01100001 1
01101100 10000111 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:
01100011 11111101 1
00011100 11000000 1
01001110 01101000 1
10111001 10011110 0
11100111 01000100 0
01101111 10001111 1
1. The parity bits for the 16 columns is: 01101111 10001111
2. The parity bits for the 5 rows is: 11100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (8,4):
10110010 11101100 1
00001001 11110111 1
01111100 01001110 1
10101011 01001001 0
10101011 00000111 1
11000111 10011011 0
For figure 3, the bits that were flipped are (3,4) and (6,2):
11000100 01011110 0
00110100 00100000 0
10101100 11101011 1
00110001 01110011 0
00010011 01100001 1
01101100 10000111 0
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: 0110111110001111
The answer was: 11100
The answer was: 1
The answer was: 8,4
The answer was: No