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 111111000 00100101
01001101 11010101
10000011 10001100
00010100 01110111
10000001 10010101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00010011 11011111 001010111 01100010 0
11001000 01110011 0
00000101 10101110 1
10111000 01101101 0
00110001 00101101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00010111 01101011 110111110 10011010 0
11101100 01111100 1
11111111 01111100 1
10001011 11111101 1
00110101 00000100 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:
11111000 00100101 0
01001101 11010101 1
10000011 10001100 0
00010100 01110111 0
10000001 10010101 0
10100011 10011110 1
1. The parity bits for the 16 columns is: 10100011 10011110
2. The parity bits for the 5 rows is: 01000
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (10,4):
00010011 11011111 0
01010111 01100010 0
11001000 01110011 0
00000101 10101110 1
10111000 01101101 0
00110001 00101101 1
For figure 3, the bits that were flipped are (12,2) and (5,5):
00010111 01101011 1
10111110 10011010 0
11101100 01111100 1
11111111 01111100 1
10001011 11111101 1
00110101 00000100 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: 1010001110011110
The answer was: 01000
The answer was: 1
The answer was: 10,4
The answer was: No