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 111011110 01110110
01001010 00000110
01010100 00111001
01001110 11000100
10100101 11011010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01110010 10100110 010000101 00000010 0
10010010 10100100 0
11111101 00111101 1
10100001 00110111 0
00111001 00001011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11101010 11010011 001011010 11101000 0
11001110 00001101 0
01011100 00010011 1
01000100 11101010 1
01100110 10001111 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:
11011110 01110110 1
01001010 00000110 1
01010100 00111001 1
01001110 11000100 1
10100101 11011010 1
00101011 01010111 1
1. The parity bits for the 16 columns is: 00101011 01010111
2. The parity bits for the 5 rows is: 11111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (15,3):
01110010 10100110 0
10000101 00000010 0
10010010 10100100 0
11111101 00111101 1
10100001 00110111 0
00111001 00001011 1
For figure 3, the bit that was flipped is (9,5):
11101010 11010011 0
01011010 11101000 0
11001110 00001101 0
01011100 00010011 1
01000100 11101010 1
01100110 10001111 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: 0010101101010111
The answer was: 11111
The answer was: 1
The answer was: 15,3
The answer was: Yes