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 111101011 01010000
11100100 11101011
00000100 10100100
10100001 00010001
10011010 10101011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10100001 11000100 001100101 11001101 1
10001100 11010111 1
11000011 01010000 1
01111100 01100100 0
11110111 11101000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10011111 11100100 000011000 11010010 1
11100110 11100101 0
10101000 01111011 0
10000110 11110100 0
00001111 01001100 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:
11101011 01010000 0
11100100 11101011 0
00000100 10100100 0
10100001 00010001 1
10011010 10101011 1
00110000 10100101 0
1. The parity bits for the 16 columns is: 00110000 10100101
2. The parity bits for the 5 rows is: 00011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (14,3):
10100001 11000100 0
01100101 11001101 1
10001100 11010111 1
11000011 01010000 1
01111100 01100100 0
11110111 11101000 1
For figure 3, the bits that were flipped are (1,1) and (11,3):
10011111 11100100 0
00011000 11010010 1
11100110 11100101 0
10101000 01111011 0
10000110 11110100 0
00001111 01001100 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: 0011000010100101
The answer was: 00011
The answer was: 0
The answer was: 14,3
The answer was: No