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 100011011 10001111
01011000 00110100
00000010 01010101
10110000 10110001
10000100 10110101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01001101 10101001 001101110 10011101 0
01000000 11011111 0
01000010 01001111 0
11000111 10101011 0
11100110 00001101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11100100 11011101 010101001 01001000 1
11010000 10010010 0
01001001 01111000 0
11001011 00010011 0
00011111 11100100 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:
00011011 10001111 1
01011000 00110100 0
00000010 01010101 1
10110000 10110001 1
10000100 10110101 1
01110101 11101010 0
1. The parity bits for the 16 columns is: 01110101 11101010
2. The parity bits for the 5 rows is: 10111
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (14,3):
01001101 10101001 0
01101110 10011101 0
01000000 11011111 0
01000010 01001111 0
11000111 10101011 0
11100110 00001101 0
For figure 3, the bits that were flipped are (12,3) and (8,1):
11100100 11011101 0
10101001 01001000 1
11010000 10010010 0
01001001 01111000 0
11001011 00010011 0
00011111 11100100 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: 0111010111101010
The answer was: 10111
The answer was: 0
The answer was: 14,3
The answer was: No