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 110110100 00011100
00101010 01110011
01011000 10010111
11101100 10111110
00011000 11011000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101010 10110011 010010011 11111010 0
10001101 00100110 1
10010101 10101011 1
00000001 11000001 0
10100000 00100101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01011011 10100110 110111111 01110011 0
10101000 11001100 1
00000100 01001100 1
11110011 00101011 0
11111011 01101110 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:
10110100 00011100 1
00101010 01110011 0
01011000 10010111 0
11101100 10111110 1
00011000 11011000 0
00110010 10011110 0
1. The parity bits for the 16 columns is: 00110010 10011110
2. The parity bits for the 5 rows is: 10010
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (10,5):
00101010 10110011 0
10010011 11111010 0
10001101 00100110 1
10010101 10101011 1
00000001 11000001 0
10100000 00100101 0
For figure 3, the bits that were flipped are (1,3) and (11,5):
01011011 10100110 1
10111111 01110011 0
10101000 11001100 1
00000100 01001100 1
11110011 00101011 0
11111011 01101110 1
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: 0011001010011110
The answer was: 10010
The answer was: 0
The answer was: 10,5
The answer was: No