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 100000101 01011011
10000100 00010110
00110101 11001111
01111100 11001000
10011111 11011110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00000011 11110011 010001011 00010110 1
01110001 11011111 0
11010001 00110110 0
01011001 01111001 1
01110001 01110101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01011100 10110101 110111011 11011001 0
10010110 01010010 1
10000101 00000111 0
10011110 10011000 0
01101010 11100001 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:
00000101 01011011 1
10000100 00010110 1
00110101 11001111 0
01111100 11001000 0
10011111 11011110 0
01010111 10010100 0
1. The parity bits for the 16 columns is: 01010111 10010100
2. The parity bits for the 5 rows is: 11000
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (16,2):
00000011 11110011 0
10001011 00010110 1
01110001 11011111 0
11010001 00110110 0
01011001 01111001 1
01110001 01110101 1
For figure 3, the bit that was flipped is (9,1):
01011100 10110101 1
10111011 11011001 0
10010110 01010010 1
10000101 00000111 0
10011110 10011000 0
01101010 11100001 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0101011110010100
The answer was: 11000
The answer was: 0
The answer was: 16,2
The answer was: Yes