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 111001111 11001001
10111111 10101100
11101111 00111001
01111000 11110110
01010111 01010111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01110110 01111101 111011101 00110111 1
11110010 10110110 1
01100000 00111100 0
00010010 00111010 0
00101011 11110010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00110110 10000100 001110111 01010100 1
10100101 11111100 0
11000000 01011100 0
00111011 00000110 0
00011111 01111100 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:
11001111 11001001 0
10111111 10101100 1
11101111 00111001 1
01111000 11110110 0
01010111 01010111 0
10110000 11111101 0
1. The parity bits for the 16 columns is: 10110000 11111101
2. The parity bits for the 5 rows is: 01100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (12,2):
01110110 01111101 1
11011101 00110111 1
11110010 10110110 1
01100000 00111100 0
00010010 00111010 0
00101011 11110010 1
For figure 3, the bits that were flipped are (14,4) and (12,5):
00110110 10000100 0
01110111 01010100 1
10100101 11111100 0
11000000 01011100 0
00111011 00000110 0
00011111 01111100 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: 1011000011111101
The answer was: 01100
The answer was: 0
The answer was: 12,2
The answer was: No