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 100111100 11010000
11111000 11100110
01011110 11111101
11001100 10001111
10100100 10000100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01111111 11101010 010100011 10111011 0
11010011 10110001 0
01111111 01001001 0
00100011 00000001 0
01011011 10101000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01110001 11100001 011100010 11011111 0
10111100 10010001 0
11101000 11100011 1
01100101 01100000 1
10101010 01101100 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:
00111100 11010000 1
11111000 11100110 0
01011110 11111101 0
11001100 10001111 1
10100100 10000100 1
11110010 11000000 1
1. The parity bits for the 16 columns is: 11110010 11000000
2. The parity bits for the 5 rows is: 10011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (4,2):
01111111 11101010 0
10100011 10111011 0
11010011 10110001 0
01111111 01001001 0
00100011 00000001 0
01011011 10101000 0
For figure 3, the bits that were flipped are (9,1) and (4,4):
01110001 11100001 0
11100010 11011111 0
10111100 10010001 0
11101000 11100011 1
01100101 01100000 1
10101010 01101100 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: 1111001011000000
The answer was: 10011
The answer was: 1
The answer was: 4,2
The answer was: No