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 111000001 11011110
01000000 10000100
01110110 11101011
10000000 11111001
10000111 00011110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10100101 11011001 100001000 00000100 0
01101010 00001011 1
10110000 01110011 1
11000000 00100111 0
10110101 10000010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01101001 11101011 011111011 01111101 0
11110111 00001101 0
10111001 01011000 0
00110111 10111101 1
11101011 11111110 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:
11000001 11011110 1
01000000 10000100 1
01110110 11101011 1
10000000 11111001 1
10000111 00011110 0
11110000 01010110 0
1. The parity bits for the 16 columns is: 11110000 01010110
2. The parity bits for the 5 rows is: 11110
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (6,3):
10100101 11011001 1
00001000 00000100 0
01101010 00001011 1
10110000 01110011 1
11000000 00100111 0
10110101 10000010 1
For figure 3, the bit that was flipped is (8,1):
01101001 11101011 0
11111011 01111101 0
11110111 00001101 0
10111001 01011000 0
00110111 10111101 1
11101011 11111110 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: 1111000001010110
The answer was: 11110
The answer was: 0
The answer was: 6,3
The answer was: Yes