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 110111110 00111110
01101000 11000101
00011111 11111001
10110111 11001011
01111010 00110011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00011000 11001011 101001010 01001100 0
10101100 00010100 0
00001111 01001010 1
00011101 01011001 1
10101100 10000000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00110110 11111001 001000111 11111011 1
01011011 01001100 0
01111110 01000000 0
01110011 01000001 0
00100010 01001111 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:
10111110 00111110 1
01101000 11000101 1
00011111 11111001 1
10110111 11001011 1
01111010 00110011 1
00000100 11111010 1
1. The parity bits for the 16 columns is: 00000100 11111010
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 (1,4):
00011000 11001011 1
01001010 01001100 0
10101100 00010100 0
00001111 01001010 1
00011101 01011001 1
10101100 10000000 1
For figure 3, the bits that were flipped are (7,3) and (5,4):
00110110 11111001 0
01000111 11111011 1
01011011 01001100 0
01111110 01000000 0
01110011 01000001 0
00100010 01001111 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: 0000010011111010
The answer was: 11111
The answer was: 1
The answer was: 1,4
The answer was: No