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 111101110 10011101
10110111 00001001
10010111 00101000
11101011 01010010
00101000 00000101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01001001 01110101 110100101 11100100 0
00110000 10111011 0
10111101 11000010 1
00100110 00111101 0
01000111 11011101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10010000 00110100 100011010 11001010 0
10111010 10000000 0
00010000 00111001 1
11110001 11111101 0
11010101 10111000 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:
11101110 10011101 1
10110111 00001001 0
10010111 00101000 1
11101011 01010010 1
00101000 00000101 0
00001101 11101011 1
1. The parity bits for the 16 columns is: 00001101 11101011
2. The parity bits for the 5 rows is: 10110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (12,0):
01001001 01110101 1
10100101 11100100 0
00110000 10111011 0
10111101 11000010 1
00100110 00111101 0
01000111 11011101 0
For figure 3, the bits that were flipped are (5,5) and (14,1):
10010000 00110100 1
00011010 11001010 0
10111010 10000000 0
00010000 00111001 1
11110001 11111101 0
11010101 10111000 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: 0000110111101011
The answer was: 10110
The answer was: 1
The answer was: 12,0
The answer was: No