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 101011101 01100101
11011000 00101110
00101110 01110111
10011111 01110011
11100100 10111110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01000100 11101010 101010010 00000000 1
11100111 10101101 0
00111110 10110111 1
00110100 00101100 0
11111011 11001100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11000011 00100110 001110010 10101111 0
00011011 10101110 0
11000011 11110010 1
11011111 01100111 0
11110110 10111010 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:
01011101 01100101 1
11011000 00101110 0
00101110 01110111 0
10011111 01110011 1
11100100 10111110 0
11010000 11110001 0
1. The parity bits for the 16 columns is: 11010000 11110001
2. The parity bits for the 5 rows is: 10010
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (11,2):
01000100 11101010 1
01010010 00000000 1
11100111 10101101 0
00111110 10110111 1
00110100 00101100 0
11111011 11001100 1
For figure 3, the bits that were flipped are (1,0) and (12,2):
11000011 00100110 0
01110010 10101111 0
00011011 10101110 0
11000011 11110010 1
11011111 01100111 0
11110110 10111010 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: 1101000011110001
The answer was: 10010
The answer was: 0
The answer was: 11,2
The answer was: No