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 101000011 01100011
11001110 00101110
01011011 00000001
00011010 11010010
00101100 00110100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110001 00000111 000101001 01001111 0
10111001 11110101 1
11010000 00100001 0
10100100 01000011 0
00010101 11111111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10110000 11110111 001000111 11000101 0
00001111 11110100 0
10001011 11010101 1
00101011 01000011 1
01011000 01010000 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:
01000011 01100011 1
11001110 00101110 1
01011011 00000001 0
00011010 11010010 1
00101100 00110100 0
11100000 10101010 1
1. The parity bits for the 16 columns is: 11100000 10101010
2. The parity bits for the 5 rows is: 11010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (10,3):
11110001 00000111 0
00101001 01001111 0
10111001 11110101 1
11010000 00100001 0
10100100 01000011 0
00010101 11111111 1
For figure 3, the bit that was flipped is (16,2):
10110000 11110111 0
01000111 11000101 0
00001111 11110100 0
10001011 11010101 1
00101011 01000011 1
01011000 01010000 1
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 1110000010101010
The answer was: 11010
The answer was: 1
The answer was: 10,3
The answer was: Yes