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 101010001 01011001
11100011 00101100
01001001 01101110
01101001 00101011
11010101 11101011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01000011 10100111 001000101 00110010 0
00100110 11011110 0
10001010 10010100 0
11110110 00111110 1
01011100 11000001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10100101 10000010 010100111 00000110 1
10000111 11101101 1
10111001 10100101 0
11110101 11111101 1
11101001 00110001 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:
01010001 01011001 1
11100011 00101100 0
01001001 01101110 0
01101001 00101011 0
11010101 11101011 1
01000111 11011011 0
1. The parity bits for the 16 columns is: 01000111 11011011
2. The parity bits for the 5 rows is: 10001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (10,2):
01000011 10100111 0
01000101 00110010 0
00100110 11011110 0
10001010 10010100 0
11110110 00111110 1
01011100 11000001 1
For figure 3, the bits that were flipped are (2,2) and (16,3):
10100101 10000010 0
10100111 00000110 1
10000111 11101101 1
10111001 10100101 0
11110101 11111101 1
11101001 00110001 0
5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.
That's incorrect
That's correct
The answer was: 0100011111011011
The answer was: 10001
The answer was: 0
The answer was: 10,2
The answer was: No