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 101000001 01000001
11110001 11011000
11100010 10110001
00110111 01001110
11100010 01110111
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00011110 10000010 001011111 10101101 1
11000101 10010011 1
00000010 00010110 0
11010100 01111001 1
01010010 01010011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11000101 01000111 011001001 00011101 0
10010001 00100110 0
00101100 00101001 0
11010111 01101110 1
01100110 00111001 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:
01000001 01000001 0
11110001 11011000 1
11100010 10110001 0
00110111 01001110 1
11100010 01110111 0
10000111 00010001 0
1. The parity bits for the 16 columns is: 10000111 00010001
2. The parity bits for the 5 rows is: 01010
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (8,2):
00011110 10000010 0
01011111 10101101 1
11000101 10010011 1
00000010 00010110 0
11010100 01111001 1
01010010 01010011 1
For figure 3, the bit that was flipped is (14,5):
11000101 01000111 0
11001001 00011101 0
10010001 00100110 0
00101100 00101001 0
11010111 01101110 1
01100110 00111001 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: 1000011100010001
The answer was: 01010
The answer was: 0
The answer was: 8,2
The answer was: Yes